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sl[41)atru'e o!" the llc.rrij ol.
irrrerrra ! ,i: r,aluiltion.
itnd tlr,: l)r-:1:iirtttrr;rtfiil
r_
,,i,i:ji,
,il rr.
iir,
"l'here
slrall lrc prr,vl,ii_li ibr urie.,,arrc.j rr
ievcl cii' teacher concerned: "liecrtnd:
('i;llcp;c/ l,)cpiu.l.rncrrt lcvcl
corul.rllrirrls
puhlicatinn of results and decisioritalteu
,
on :irr('Il ti,-.1:i5lfun shnll l_re filed
in thc IJnir.,
,irri \\,uBli lirr,-l Jer:i-sitrn tlkerr rvithin one
tl
grlevartce redr.,ssnl rvill he announced
by
the
Univ:rsity irr
e , as fi.red trr, 1 ,a Syirdiglirt.
r
arivance
l.,romralization of continrre:us
irrternal e
thcr"c is inilation ul' mlu.l<.s iir
interr
propoltiorrarel,y iI rhe vtriation
L]etwee
2.
-.t.
rf.
.cvirluttiorr ol'clisr-crti.rtiorr rviil bc dorru
t.ry
ical examination (exrerrral) ar
tf,., *,,ci-J.;ri
plgject reporr r,vill l.re a.r t?illorvr;." - :'
I
--l
I
Preserilation
-'stions
t.,1
I
iy,tr er
iqf1
ii,ii,rJ .iuir.iii
i,
Pnss requircmrnt: .l.he
.' i"
;-,i1.q1; llilr]lt)lr,ltlt l0r. cach
llaper rvill bc 40%. 'l'hcrc
separilte rninirrrur-rr fi_rr. int.:r.,ral
c'r,Aluirtior.r irr:tl ncl provisiort lbr
it n;tr<l ver
rrerrt.
.
fi.itrrr.. iir:.ii:: [,1
will i^- rro
L_ .\
7.
Classilication o I Results
!_C_!g1r yit htt isrin;rio;
I Cllass
:
80 % and al-rove
6096 and aboyg antl belorv
II Class
III Class
3.
C1.,5,
rt-,o.e-"".-rd
periocl 'uvill be
rse.
^:-
l4Oo/^ ttrrrl .h..',^ r-..r^--2I"7
c.',
I0. Supplcrnentary exanrinatirrn
ol
thiled
can
seulester c.ramination, ciul
appear fbr the fa
the regular" strrclents. .I.rvr
srich supplernen
eaclt senrester.
g09,o
-.------- l
t appearilirce n'ithin thc:
rnarl<:i rcceivcd lor tlrc
-
t-l
lrrtrrrrll I,,rtcrrritI
l0
tJ0
I
i
i.fr.E
r
irn([
lrx)
80
.J; /\nalY;is
?9__
2o
ol;ll
100
8()
rt0
60
j
I0
rl,-i, _1 t..tjt,i+c,t riaiGl.iL
2. li_$1()cllq$ t ic pro crsses
ti0
li
-ql]_
-iI
-;r,o
too
ltr;
t00
'100
ll0
l
t
100
80
I
i
60
!!estel
in
:.5_r practiciit tt
(]
r
a,rct
r00
l(x)
starisi..ai t=",rrlt,rr[.
t20
_5,80
80
rJ0
i!, ii i.*rlr
l0()
I00
--
|
I0()
r00
irrl,sli ilr
t00
.V itn,ii- v.;i,r,
-50
_
___q,__qlq1'orrrt
*'t-Tiilf,;-:ii:'#l,l
l.
sxpers itt. iie,re'ster
ficonornetric MethocJs
.1.2: Opcrations
ll.esenrch
.[.3; Econornerric
2'
c'onege
I
{( )1, _ I )
(Ol-] _ -l)
.1.4: ivlarlrernarical
Ecc,nornics (Op _ 4)
4.5: Pra.crical III (Based on 4.?
rt._.])
and
statisticnr err,rrity cont"oi
+.
{:
Uperations
4.3: Operations;
:
J.
fu1ot1,_,ls
IV..
o,ubp*ratio,s
p-esearch I (Op
- l)
^.csear.crr.
II (Op _ d1
.lrttnrl
i
((
Resear,.:h
,[ ,l Strr istir.lrl
errirlit-r,
.1,-5: [)rlrclierrl
lll ( l]irr..,l trrr
)1, lt
I irir,l t.-l)
IJusiuess anrl Inc!ust"iul
Sti
tilti.j,,.
'
:1.?: (J1.it:ririiurrs
I{,:sertr lr I (( )l) _ I )
-1.-ll lritju:ttri;rl Staristici
(Op _ 6)
-l l+i Sjrati::riciil ,i,,,rf
li',l, irnrr,il ,r)1, 7)
4.j; prrrcrir:irl Ilt (l]aset.un rl.l.
Q, Actuarrit! Scient:e.
,1._1. .1.
{.-.1 irrrtl
I
_l)
4.1: Srrrvival ,{rralysis r Ot, _
_t)
4,_t: Ai:ruarial Nratirernarics
I (Op S)
..1.4: Actuarial
Ii.Jathemarics Il (Op _ o;
4.5: practical III (}-lasecl * +.:. ,1.._t
anti l.-l).
/ Departr:rerr utir) or.i.er.
4.yi1..
,,j
ttrc
events
-
Fields and <;-llclds
cllls.: ,ri't.r crrt,,
lirrtits,,l rillrrl,,iir
lirnctions -- ranclorn vitr.illrlcs
\,ar.iilbles.
l,l[_
,,:;li[",i],1.;:"ii;i]:1,,1,,,x,,,ijl,,i,,
rrliriorritl prolr:thilit.r. rrrcll:;tlrc (
4.
,,,lll,;i.;,,; 1,,;1,:, l.
rr11y11j11,-, rlrr..ir
.lu..
i, i,,,.,,,,
,iii,l]I,"l] ,,ru
crcrrcnrar\ ,,..rJrr_,rrrr.:. i),.e,r,f 111,, ,,;1i,,,,
tir_rtt thcorelrt) l_triiirilrrtiiirn i1r:1,,j ,, \,
,1
I t.
7'
Characteristic function and rnoment.s _ lrorrr€
Convergence
of ranclom vadablcs:
cleinverg,ence
irr pro[rabilitr, ('.rr'erucrrct.
\ \rrr\
;rlrr,r.;r
''
,-i,i ,i;.;;,'8. Cottvctgcncc oI rlistrillrrliorr firiclirrrr:
Wcitli lytrl crrrp;tlt:t(: ((]1,,(_.1r,- 1..r_. I lL,il,
cqnvergence, tlreoreln
l elly-Bra.v lerrrrra - f.lelly-Brav rlrcor,lr, (..rr,(.,-lrr.,.r:r,
distribution hrnctions arr<l cl,,r.irc'tc.i,rti. li,,',,,;,,,r,
,., ,t,,,,,i , ,,,,,,.,.,.,
9. Ilttlcpcndencc: lnrlependcrrt.c rrl cvcnt.\ (.lu.ss .,i,','ii,.,,,i,r",,.,,],',,.,,,i1,,
ol. irrtlcpcrrrlclrr L.\.(_,lrl , iltrl r1.!t.;iq,rq,
classcs-lndcpenclenccof ririttklrtr varilrblcs
lluhrrogorrt 0_l llrrr lJrrr.cl.s()..i i.111(.1
surely
-
Corrvergerrce in disr
ributio.
('.,n.,cr.ger-r." i,,
r
l1-.,11
i1 r11
ro\,'s inlqualitv
.
arrr-l ir,:.,. (-,rri.(:,r.rj(.ll(.f
rv ol'llrrge ltrrnrhcrs 1iir.l ,.;lr:ir-, l..irrrrr,itrrr
Kr)lrrrogorov SI.l_N lirr iiil r.:r:ic
nrr
Text.Book:
I' Il'R' uhat'
i\lodertt Probabil t1'-l'lrcory
-
(i"r trd.).
LiaPlrt.lv.s
lbrrn - l.incletlr:rrr_l.r,llcr
tJc,,v z\,gt i,rrtrli,:rri,rr:r r
I
,
[ht],,r.r.r,
,),i,,; .
I Semest_cr- Paper l. 2 - IVlcasrrre lrrd tnte.<lratiorr
l.
Nlea.srrntblc
Frr.cti.lrs:
N.l
,:rli.rirlrlc:ir_.1:i
l, l,..ir:;rrr.rtltl,.:
lirrrcti.rr:; ;rrrl tlr,
Irrxtst evcry rvlrcr.c
4.
properties of
,
, , i,rii\rr;rl:r .
(,lrirru,:s
ntegrals - 'l'lre irrtcgr.al ot. lrorr_rr,_.!liu r\,, ,., ,:r{.n,1,,,
ntotle conv'cr8ence 'l'lteorr:nr l';rtt.,rrs l.ernrrr;r
integral.
Integrnblc frlrrctions: lntcl:rirblc rc.al valucd
lutrctiulri .l li*
integral - The Lebesgue Dt]rrrinate<r (-onve-rg,cric.-. ;t:t,",.,r.,,, [ro..;ilii,irr arrtl lirrr:itrir,, i,t
rnrcrrr.irr:; r,,rricrr tr,l,,,1rrtr
parameter.
!
ilr_,
ol
,
Splces - tlre [-,, liplrccs [[oLlur ,; lnr-.r;ruriitr
'flrct.lrern . 'l'lrt:
splcr. L.
l-,,
.?,,:ff,,xli:',,ion
'r.he.re,n
-
!
r,e
-
(.'tlnt,ergerr'J('
i,, 11cil.S1rc ,\lrri.st
*"0",-,r,ll'i'i-'?,T:lli:,.'"-:'111,,."''"'"1,1
s: fierltt'ation of lvleasures: i\ leasures orr aluebra,ol'scts[he c:iterrsi.lr
Caratheodory ['lxtension theorem Lebesllui
n,,,.tit .r,.r;5urt: liri,:!ri,.,1,
^
9' I)ruduct trlc:lstlrcs:
l{ectanglcs
Class l.enrrra .- Tonelli's Tjhi:,rrerrr
,ubini-s
Robert C' Bartle' l'he Elernerrts of Inte-urati<ln.
.lohn
'Aliprantis C'D. ani Btrrkinslrarv
( r ee8).
t)i.r).rt;rsrrr.r,
I'lrc pioduct ivlcasLrrc I lrcor.cra
5r)r:rrrrrr,;
.[.lrt:t.,r.err.
__
Reference Books:
l'
,,,i']:;,,, il]iil.:;l
r
rr,
1r:,.;1q11;.,
Text Book:
l'
,,
(.lrrri.rrr-r
o.
Principles
wilel
-orr,.l
ijr,r;.
, ,.i rr. \ rr !rr, rrii.
i.j,:,,r .r.r.1
r)t'l{eal ,,\rralv:iis ( i,.r I,,1.) z\crrlt.r.ir
2. Ilana l.K. Introdtrction to Nlc:rsrrrc iurtl lrrtcrlnrtirln.
NJ;rrosrr. 1..]c\!.
lr(.llri
l;rr,..-
-(,
lysis
c t_rl'tlrc. irrtcgy:rl /\"rrcccssary
antl
ortflnt thecrrerird _ l:irst rneln valtre
le.
rvith finite lirnirs of inte.grarion
i^tervul
+'
sel'ie.s
-
__
Tesr
appr.c
serits: t"tioJic
,1io,.i:.:.-t
.,.;_,
,r_,l,l.pletrness
nce _ Uniform convergence
on An
rifbrmly convergent sequence.s
lbr r-rni
Weistra"-s
and
firnctions
-
Fourier series fbr e,err *ncl
ocrd lirnctiorrs
. 'l.i\I. Ap.stole.
2.
Rudin.
W.
I
(
IJY*')'l't't
I.rarf range
tious anrl.,.l:*:r,rpt.: _. Open
antl ciosed
_ (_tonvergence and
I Co*p0,,,'ess arrdset.
connectectness.
..\r.tira
(leee):
Marhemarical .\.nirlysi.:;
q..1,,,,
Itcfi: rerrcr: Ilooks:
I
-
-- Continuity,
arrd unilbrrrr contirruity
i;;j;;,,1,,#,ll,.irl,;,;]-"',,ra
lVtathe rrreticirl
prirrc.iples
c'D'
ancl
.\rillysis.
rl'rt.;.
i,rerr, ,\ut:
Naro:;a ( l(rti5).
of Marhernztrical Analysis. IvlcCraw-Hill
(
1
926).
Il'rkin: haw o. Principles of near
Anarysis (3,., Ed.).
Acacremic press
isson
ion
gnornral distribution
applications).
-
._
,r.?lri
orn variable _'Expectation
and
ofrandom vectors
cation-s.
rution -_ I)istribution
'l't:rt lluok,r:
'.la(rri\)r)s
alrd
_
variates _ Marginal
nts _ crrarlcter,istic-
rrr(lrnents.
i ''!i:;:H:r:?ii.;
Apprcarions (2'*' L'-d')'
w,ev
Eastern ( ri,riie),
e theory of Statistics{3,.r Ed.).
aa
. (Chapter 2).
athenntical Statistics. Wiley
ory of Staiistics. Vol.
:#: li
rrttrltivrtrirttc sluristical
.rurtysis
12,'.r
cd.;. Jotrn witey
I.
_
.n<J
@
1.5: I-inear Nlodels
I'
2'
Vectorspflces: Vector spirces and subspaces
fnner
products.
.
-
Bases
an{ cJimensions
-
Linear equ1tions
-
M:rtrices lncl linelr equarions: [v'l:ltr ices and nrarrix algebra siystenrs t,l linear equati.rs
inverse of square matrix - l)eterrni]ants
S;'stcm.s r:f lincai eqrralion:i -. cjcrrearalisc<l
inversc ola rlntrix - lvlatri;r representatiorr of vector spaces.
bases ctc.
Idcmpotept
-'-llte
"
n.ratricL,s
'
-- Kronecker product and Fladrnard product.
"
3, Matrix Ilornls: Nonrrs ort vector spaces - l'iorrn:; on sl,a*l:i ol'rrr.trrir.r:; I)r-ollertit::; ,,1
operator norms - lvlatrix lrrnctions cletiu:cl -- t]anach I_crrrnra (crilcrirrrr
lur iLrrr:.rtibilit_v)
Stability of algorithm.
4' Iligen values antl Eige, Vectols: Eigenvalues o.nd eigen ve.lorj - [r,lr()rr;i,t
5'
(t,
eigen values
-
Eigen values and norms
-
properti*s
t-,1
Polynorrrials iri a nrairix , [)ii.rggpi;:irl,rlc ruirrricci.
'fordan canonical hrm nrtd applications: Nilpoterrt rrarrices
Applicatiorrs.
-
Jordan canonical lorrrr
-
Symnrctric rtntl hcrnritirrrr nrulricrs: Sclrur.s rrrritul.y
trirrrrgrrluriz_rrtiorr Ilrcorcrrr I{cal
quadratic fortrrs Ilermitii n fbrms IlcrJuction to
diagonal lir?rn - I)ositive-rJefinite forrns
and matrices - The signature of quaclrat
.l'p.ir
Eigen varues ancr Rayreigh,;urtir:,r
of fbrrns
(.o
-
i,:jT,:il1..l|:l.rrr
7. lin:lt ['rognrrrrnring'Pr,rtrlern: Crap
,plex rrrerlrrrl (.Sr.arrtia^l lbrr.
Dtrnlity Sluck urrcl surplu:; varilblc a
r'ctlrod) - 'l'riursportatiott
pro"ble,n - Assignmcnt protrleur Traveling
,3,;' "t
B' Ganrc theory: N{atrix galnos - reduciblc lo 2x2 nntrix - graphical solutions ('oirversion
of
games in to
_
I'ext
tsogks:
Lpp.
o l' C'R' Rao' Linear
.
Statistical lrttbrence and its applications (2"'r
(Chapter t).
2. I,ervis D.W., lv{atrix Theorr. Allied
^
, "Pf::.:,:,:.1.:::1,:,1
.*,. ?l
Ner.v Delhi. (Chapters t.. 6).
i;t,', M;;irir,'i,,uii,i;'l,i
Chapter 2, 3, 4.1 tc 4.4, 5 and Section I 1.4),
[id.). wiley [..astern (lqB9)
ffilrl;;:lr.*
0
y.rk
(part
r
rs,..; r;.!rrirrrrrg ur.rrrrurrrr()'rar: rOpl.llatlOn allcl Salflple - UlStflbUtiLln Of'SL
:lHrir,rius iirid srrrrlilinil di:stributir-ln - Sarnple rnoments - Sample mean and varia .,,i
ijr,rlplirtq fir-rur nonnill disrritruticins - t, [r ancl 12 clistributiorrs (central arrcl non-centr,
I'ii:;tril-rutiort of Quadratic ii-rrrrs - Order statistics (distributious oltilnctions olortie, srat!:r.
'
-'
2.
,
as)/mpto ic 'cli.stribution (asyrnptotic distribtrtiorr
of sarnple qutrrtilcs fis-ycrptori
ol t, F arrd X-J ( te:xirig in nontrill
disrribution of exlreme value statistic) - ,{.pplication
distribution) - large sarnplc tc$ts (standard cror - nonnal tests - 7"2 tcsr. olgoodness oi'fit).
G:russ lvtlarkov lincar modcl: Gouss.Markov linear niodcl - Estirnability cf, paratnerers Gauss-Markov theorem - Estilnation of o.2- Analysis of variance of orid way, two way, rwo
rvay rvith interaction : Ani lysis of covariance (one.way and trvo-way with single auxiliary
variable).
3. I-inear
regression nnrrlysis: Linear regressicln models - Least. Squares Estirnation l)roperties tll'l..eust Squarc list irnirles - llstirnatiorr ol'o,2 - Ortlthogonal Strrrctrrrr: in tlrc
l-lesign lvlatrix - Cencralis-'d L,east Squares -'l'he F-test tbr linear regression - Multiple
Corrclation Coell'icient -'.ioodne.ss of lit test - Analysis of residuats (Definition anrl
propelties of residuals - Re:;idual plots - Statistical tests based on residuals Partial residual
;rlots -.'i.r-tnsftrrrned
residuals'lrrnslillnirrg tlrc datu.
'1. llolyttotttial
regrcssinn (sirrgle explgnatory virriable): Fitting of polynonrial (Least square
theory) - Problems oF ill-oonditioning - Ctroosing the degree - [i.tting r:f ortlrogonal
Polvnomial (Ge nt-ral Statisl':cal l'ropertics .- Cerreraii,rg orthogorul polyironiials - Weig-hted
lc'iit:;t S! tlitfr,:3 ).
'I'cnt l-iuulir;:
o
'
I
(
'.ii. lr.lir. I.irttitr :irrr1 i:itiu;, I lrrl'urcrrr.:r: irrltl its ApplcaIit,rrrs (f'"1 l:d,). Wilcy Ltustcln ( 1989.1,
l.levi Delhi. (Scction 3b.).
). ii-D. .loshi.
3,
Litrear Estirnati xr and Design of Experiments. Wiley Eastenr ( )
Sebcr 0.A.F. L.irtear ltegre::tion Analysis. John Wiley ilnd Sons. (C,'hirprer -l
luptrt ).6
(;.6).
4'
611111.
Sir lvlauricu Kendull artd Alan Stuart. '['he advanccd tlreorl
o1' Stlitistic.s. Vol. l.
Disrribution l'heory. (4'1, Ed | (t917) (L-hapters 10. I l, l4).
Itohatgi V.K.^en introduction to Probability 'I'lreory ancl Mathernatfual Statisrics. Wilev
5.
Easrerrr.
Newilelhi(19g0).
Cihapters
2.
4 and 5.;
lleli:rcncc IJooks:
t. Klcinblurn, ti.ttllpcr, lvluller lnd Nizarn. r\ppliecl regression analysis and otfuer multivariable
rrrcthods. Duxhury Prcss. Nc'v York. (l()q8).
ll Scrirr:slcr -. lr:r1lur. 2.2: l)ar.:rrrrcr ric csliruatiorr:
l. Pririciples ol' Dlin llccltrr'liorr: Srrflicient stutistic - Sufficicrrcy prilciplc Minirnll
srrlllcicnt stiitistics - Ancillary statisiics -- Sutilcient, zurcillary uni.o*pi"te statistics
I iktlihocid liirrctirin - [-ikelilroorl principlc -l-lrc invariauco principlc
)-' Nlirrinnrin v$riitnce unbiast:tl csiinurtiorr: Un5iasedness - Best Linear Unbiased estimator
C'rnnter-Riio Inequality and irs appliqations - Ilao-Blackwetl theorern
Lehnrann-schetfe
tlri:orerrr -- A rrccessary arrd srrllicienr condition tbr MVUE.
lo
I Sinrtilt:riltous estinlltiort ol'sevcral pirrilrnctrrs: Matrix optinrality crirerion - Ellipsoicl of
coIIcL'ntratioi - l':leberrov- -.innik-Rultin Tlrettrerrr
- Craurer-Rao lnequality - A briel.
r!ii;e ussi<ln of l\{, D, 'f and E rptimaliry.
.l ,,\..;),rrrptr;tic prr;per"ties of r.stinirtoni: Clonsistency _ Methocl of rnornents _ lvlethocl
of
lrfri:t'rttiL:i; Clrui-rr;ing lrctr'scii corrsistcrrt cstirrlators - C]orrsisterrt Asyrnptotically Normal
(
5'
t_'rtt,t
i llsri nriitors.
Mctlrod ol'uutiirnutn likelihorlrl
6
Lner-l-lruur
[Ji
(t\'lLtI):
Definition
-
:""ffii:ll:'j
intcrval:'l
intervals.
l\,lLH ifl exporr:ntial lhnrilv and
rh
ctll
.,,#i:
Bl
ng
8c
ill
'I'ext lloolu
l' IJ'K' Kalci 1199!)): ,{' ilrst c()urse on pararnetric inference; Narosa publishing Flouse, Nerv
Dclhi. (Chapreru 3.4.5.6.7 l0)
l. (jcor$c Cnsellu and l(oger I_ l]erger (1990): Statisrical lnt.erence; Wadsworth and Urooks,
Prcillc Crove. Calik\rnia (Clh.tprer 6).
lLe{trence I:}oolts:
I. [:.L. [-elrrrrann : 'l'treory ol'l)oint Estirnation
J' ir'l' l. Wrrsan (1970): Perirrrlctric Estinration: McGrarv IIill.
Nerv york.
0.
?e
II Srnre.rter-- lrapcr 2.3: .l.esli,g
I r\'rerrrods of finrrirrg i*,.1 ol.statistical
"i.ir"rihood lrypothesis:
rario tesrs - I,lvailallt
-section-,nion
tcsts _
tcsts.
2.
litie
te.sts.
3' ivonjpo*nretric fjtat
-
(Jniort-
er Iirnctioir _ l\,L.,ri[
nd
poivcrlLl
Ila-ycsian tcsts
J.,rrr,*,,s1fi1]
hin Theorern) i,,,i,r_l.l
'
''sol
)lirnil;rr
16
'
')r'rrrrirr" I.al
1*_,r.,
ir._i
l r:r:.111' rrtosf
tests (The I(olnrogro
Trvo Sllmple tesrs (T
Ttre Metli;rn test _ .1.
test of independence
Sornc liutdalnental idca"s
ol. sctlrrcntial samplinyl _
quential esrimation of
mean
popul;rtion _ The
"fl, ,"r,l,rl
properries,, r spRi'_";lm'
il,, rar,,,,, urir I
ir,e,t ir r
H::*",
iti"Jl::%;
(leeO); statistical Infbrencei
wadsrvorth and Brooks,
rnethod.s irr Statistics.
I
i.
ti.L. I-clrrrrarrn
;
.[.heory
f
ill.:1T:ll,irr.Ju."ry
ancr
rvrathr:urar ica
I
srar
istics. wi
rey
ol l)oint [stirnation
2.4: Stochastic processes:
' iIx[::",,"
corrccltt ttl- ;tocha.sric
[)r{)ccs.s
- c.rarn;rrc
:;pr:cifir.,^rirrrr
,rr
:.r,r.:rrp51is
nrl, _ one
step rr
transition prohabi
.- Linriting
probab
rn traisitflt stales.
n.s _- Ivlean alrrl vurialrce _
pr()gerr\,.
ribrrt ion
_ I)oissrtn
proccs_s
e.s _ l'hc tran.sition
l.rrobirbilit,
g transitiorr
l>rohabiliii,:s
s - Di.stribution ol.N(t) _
L,iurit
Exponential nrr:Uels(NliM/f
. fra)flfZC arrrl (lueing sy.sierl
"l'U.,,r,.,r,
eues (open system
and closecl ,rri,r,r,f
rcept.s
I_litting times, rr.r;rx
,\vnian nrorion (Br;;;,,j;;,
rns of Brorvnin,, innti,r,
ip,ri
]
!];li'llu;::.:Ll*
i.t 'H'i"ll:I::J[::ii
: tochast i. p.r..i..r,"J"1,
*_;r.,i;X,-dhi
3.
4'
S
A
S. Karlin.tr.,
l;r,lJls.ai)
ilttrl
!,'crrnretric
Acac'cr.ir: r,rr:ss ,,,,, rr,,,,,,.,,n
.T-ayJor;
in Srochirsric pr'ct:ss,:s.
r',..,i"rtiriiy iri",r.y'i,,,i'i*ifpt;r,otinnu
Vor.r.;rnrr Vcrr.2
!
2.5; pracrical I; praoicnt treco.r .... _-.-i, utr.r,*",r i,, ,,." ;,,'i,_].iil|ff],.!il:il,,li, ,urr... ?. I to lr..r. i,,r.rr,111.11,,r,,,rrrrrat,rte
Paper
-
cjarrrbler's ruirr
ge r nterrar io na I.
Firsr cour.se
w' I;e'cr: A. ll-l:-,
irrtrocruciiu,, to
.1,!_".Tt,*,'scicntitlc
ci,lc,,tut.rl
l,lici I
_
/
I
. :.,-lrrririirrdr{ :riitl siiiriiili'r!:r 'l;tr'il""iji,?')
_ lo
""""'"""^
^-. r
-
a.
lll -
3.1: IVIultiv:rrjal,: Analysis:
Alr overvierv of mrrltivariltc rrormal distt.ibutiolls.
'2. llstirriatiorr of ureatt vector and covariancc lnatrix: ]'he
mtrxirnumlikelihoocl estirnators ol
l}te tliean ve(:tor and covaliance rrlatrix - 'l'he distribution of the sample mean vector
lLtlLrettce concerning the rucirrr rvhen the covariance tnrttrix is'known - properties ol
Senrester -
l.
l.
.l
.
t.
L)utilililtors tlte rnr:arr vector.
l,riritrilltrtioils :rn(l use$ ol samplq correlation coeflicients: Correlation coefficient of a
bivariitteiirntl:le -- lrurtialc,,rrelaticrn coel]'icients.- Multiple correlation c6etlicients (rrull case
orrlv ).
"l''hc tlistributirru
of the saruple covar.iance matrix.:trrct the stntple gdaertlizcd vlrioncc:
'llre Wishart riistribution'- l'roperties
ol'Wishart <listribution -'t'he geniializerl variance.
'l'll* gt:it*i':iiirar,l T'? statirlics'unrl its distributious:
Derivaticxr ol'generatized l'2 statistics
(-lsr-rs pf"l'lstatistics -.'t'lre two sample problern ivith
:rtiil its
trnequal coyariance
'listt-ibirtii;trs
IIiilti
ir.
iCcg,
t-'lt:;sificiititirt
of
ollsrr-vntiotts: The problem of classiticaticll - Standarcls of good
of classiflcation into one of tr,vo populations rvith known
Plotrubility clistrit;utions - Classiticntion into one of trvo linr-irvir lrrirlriviui;itr irL,.r.il,l:!l
poptrlzrtiotts - Classiticaticin intr: r.ltte o1'trvo nrultivtriiue nounnl populurions
wherr pararneters
zire t^stilil:lleil ('leissificirtitlrt irito one ol'several populations Cllassilication
irrto o,e se'u.irl
c:li:.:;sitlcetiotr "-. lrrocedures.
7
lLrulti vtiriirte noruurI populat ions
Sorne tikelihoorl raiiritests: 1lsting inclepenclence
of sets of variates l Testing equality ot'
'l'esting equ$lity scveral rnultivarilte
nonnal popriatio,is '['esting
t]re liypothesis t]ret a covariance rnatri* equal to a given marrix - Testing the
hYpcithcsis llrilt il ct)vilriitrrc,,' rratrix is prclponional io a givei matrix (Sphericity
tit) Ttsring the hypothesis that fl rrean vector and a covariance riatrix
are e!ua) to a given u..io,
arrd a rnatrix - One rvay and rwo N,IANOVA.
PlirrciPul corrtl)orretrts: Po1:
ipa
nts -- Surnmarizing sanrple variarion
try prirrciple cortrptlncnt - Arr
edr
ulatilg sample priricipal component.
several covariance rrntrices
c'
9.
[:rctur ultillysis:
*
On]rogonel
estimation
sc0 rr.,s,
- Iractor rotarion -- Factor
'['ext I]uuks:
l'
T'w. Andersori: An introduc'tion
to nrultivariate statisrical analysis (2*;;.). Jotrrr Wiley antl
liorrs, Nerv I ,iri., ( Igit.l)
l?-ii:hlirC ,\.. Jolirrsciit tintl Dean W. Wictrerrr. Applied multivariate
sratistical analvsis.
I'x-r,rir.:r--llall uf Inrlia pirt. Lrr.l., I.icrv Delhi ( l996).
'l'
' ' i' (l'li' Raii
I-inear Statistical Irit'erence and'its eiplcatlons (2^'i
l"lerv l)elhi, (t:hapter B)
[d.). Wiley Eastem
Rcfcrenr:c lhioks:
I'
Ir4orrison t).IJ. Ivlultivariate Sratistical Iv{ethotls. IvlcCr.aw I-lilt,
Nerv
y6rk (f ilol.
(1989).
- t) -
Il-l
-
Senrester -
3.2: Analy.sis of Siarnple
arrcl
_ Hielcls
of Sampling Theory _ Ir
disarlvantages
iimple ltandorr S:rnlpling: Simple Rirrrtlorn
Si.lrrpling
o
4.
6.
B'
^9'
l'
rvithout replacemerrt - Estinrntion
of"rotar.and
rcplacement - ord:red estimrt<tIs -'-
;;
c,ir,
p*.-rr-,I-',,
ii. s"*purrg varian
l-,,,.
. ,,,,,, ,rn
r;iun1,-rint
o,n,ir
tJntir,l,,r.d e.stirrr;ri0 ; -- pl)s si,r;tr:r)ri"rrir; sarrIirri:.
l?ati. ILstinratorx: Ilatio rrretho<l of estirnation
__ flir,
.,f ,r,i,;,._.rl,rr,irrr,, i\ir,ro,ti,ratt:
variance of ratio estitnators - (-jomparison
of ratio estimotur. rvith rrr"e:ur per ulril
clonlldencc
Iimits - Ratio estinratcrs io Ilttatified
sampling - urui.5.,r ratio estirnaror
anr.l
it.s
varia_nce ..
UnbiasiO ratio+ype estimator. _ product
cstiinhtor.
l{egl'ession E.stinratom: l)ifl-crence
estirnator _ Regressiol estilltal.or .C_iornpnrisclu witlr
mcan per trnit and ratio estitn rto.s
Regressi.n
i,,
cluster sampling: Equal ct,ste*a*pling
"rrl,r.,nl.. i,"-1ffi's;rroi;),r.
lrst;matio,r of nre,n ilnrl its variance Rel^tive
efficiency of-cluster sar in,,
opri,*,],
iir;ri..''sir.l -- Lt,,c,1r,ar
(E'stirnators of mean ancl
sarrrpring
r ueriancc - Relativc efficiency ol, unctlr-url cluslcr
"rurr.,
s,r,plirg) -.
probability ctuster rnpting.
Yj.I,:g
lvlultistagc sarnpling: sarnplirig p,-"o"*dur.
-.'frvo srage samprirrg r.vith erirnl first-slage unirs
(Estimation of tnean anct its
'.,'uIi"n"* - optimunr all"ocation)
- 'flrree-srage sarr4rlirrg rvith
;:H;,,:0j:t
-
Stratifie<j nrultistage sarnpling
(Estirnation or mean ancl iis variancb"
i\'[uiti-ph*st
sa.nrpling {irr
foL re!:,re,;siorr
sa
dil
es
Non-sarnpling
errors:
- Two-stage sarnplirg u,,ith uncquur 1-'st
- oftin,ui oir.,,,'"iiofi - r.,ro-,nog."
np,
: Do,rblc sarnplirrg lbr str
-, oprinrar ailocaric.,n - Doubre
estin.,ator _ O!yU[ .norpl
i6 e51i1r,*,,r. _, nouUf" sarnpling
_-Dorrble sampling fbr pps
o
sourr e and typesif ,,.'rn-*r,npriirg, crrors .
I-Jia.-.c"r ani.l viiri,rirl,,. r.11.11fq
- Non-sarrrirling bias - Norr-tover.age-(irrcornptere li.arnei anrJ
nrissing
rrnitgt -_ f.l{)q-r.e$,ir?1,ie
erors - Techniqrre for arijustrnent Jf ,*,,-..*po,-**
,,],,i,ri,,1,,, i,r,:;rjr)r.rri:jr
-"1;jiitr-,-i,,r,,ror,[
errors
fiespr.lrrsc bias and respo.sc variancc
[.:.stinurri.; ,;.^r;;;;;c1,"',,,,,,,,.,,,,,,,,,.,
Opt inruur nu mllcrs <) f cuurrren
to rs : Tal:rrlat io r errors.
Tcxt Book:
-
r
r
Anar,vsis orsarrrpre srrv+v L)esigns
iiX-Ji[! I;l#lilf lfilJg5f*
ILeference Books:
. Cochrzur W.G. Sarnpling -Icch niques. Wiley Eeastern
3"T,".fl
1
2.
ol
Systeid^tic Ranrlom Sar'pling:
Sanrple helection
-
I
s
,
of Sanrple Size.
Ranrlom sarnpling: Prirrciples of
stratilication - Aclvantages ol srrarificzrtions
Estimation of population
and its ,uriur',." - nrro.u,;on of sample
-."i
- Relative precision of stratified.R:lrdol: .tlrro,'* rvith simplc size in difli:renr. strata
ltarrrlonr s:rn4rling in prcci'si'trn due ro Stratiflcatio,. io.n.,ation
of:strarn--Dererririratir:ri
fillilj:irlfgain
or.
equal probability
l0'
pre
Arl,antagcs a,d
disaclvartaties -' [j:stilnation ,',i'nte{ln
.trro.oJur*.,
ancl its sarnPliuI vitri;lncc
(.]p1pp11i51,rn
.{ q_vslcrrirtic
rvith straiifle(l rrltldt)nl sit rrpling '- lnlerperrct.,.'ting.f
ri.-,,aric sarrplirrrl.
vur'5'i'14 r'r.r'rrr'i!i{y S,rnrptirrg:
l)roccdures or. selecting a salr)p
alicln of..r-ota
its s^nrprinl; virriancc in pil; Jampring
rnitrr r"piac.r,r*nt ps.sarrrnring
replacenrent -- pps sampring
rvitrrout repraccment -
:i
7.
__
o^,:*n,kt1']'j;,,i1'l,l'li'r,Lf,J,:.?,f1fi],il11;:;l;,L"H
E
3' s
I
ni
Survey llesiqns
L llasic Concepts oi. Saml>le hu**yr,
Cen.sus
Sukhatme I,.V. and SukJratrne
.
( I gg2).
B.V. Sarnpling theory oi-.,ru.yr rvitlr applic,ri.rrs.
w,ey
* l*I
.r,
,.i,
.,i.
l{l
- stii**r;ter- -
t.
7.
l.
,t.
' a,-
6.
J"3: fiesign alld iilllilysir of lixptrirnents
(Jogi:t1tts ot' Oxpeinrents: Dlsign of ixperiments and collectitrrr o1' riiits -- L:i;ipetii:iet'rt-s,
rlreir detign iinrl irnalysis - I'hree principlcs of Desigrr of tixp.:rirncnts - L,rperirrttntltl ertt)r
urcl irrrerljr-eratiol of dara - Contrasts - Ivlodels and aflal5'sis of variance '- Analysis of one\ryay, [wo rvayan{ three rvar classified data - Orthogonal and non-orthofonal data.
Cornplctc Biock Dcsigns: Cor:rpletely llandorrtized Design - Randornized Block Desigrr l-.aril Scltnre Desigl -- Ir.lerhod o1' arlalysis of experintents rvitlt missing observations (I{BD
rurd LSD).
liirctorial llrllarirrrents: f'actorial experiments and varietal trials - I'actorial experiments
rvith tactors at two levels - Finite tields antl design of experirnents - Grouping for interactiou
conira.srs - Courrlbunrling - CounloUncling in urore than trvo blocks -- I!.xperiments lvittl
lircrors at tlrree levels'each - General ruerhod of cotntruction of counfounded lilctorials .lvlaxirudlr nurnber gf factors to save interaction up to a given order lbr ir given block size AIral1'sis of- lirctoriaI experirrtcnts - FractionaI factorials.
rl:;yrrirnetrie;il l:rr:turi:rl erlleritnurts ulttl split-lllot desigtts: Asyrtrlnetrical lirctorial design
-. Corlnfoundr:d asymmetri,;al factorinl rleiign -'Ccrnstruction of b?r'lanced counfourded
;r.;1/irrrrrctritliil fert:icrrials - Construction of asynitnetrical t]t(:IDrigl vx22 it fv plot blocks ,lirril-.1si:,Lil-ialani,.:il couriftrurrrled asyritnirrirical factorials - Sniit-plot desigrts - Analysis of
lii;,iit ililr,lrrigrru.
Igctiurplele bluclt desigri-t: Irrcornplete block dtsigjns - Ilalanced Incomplete Block Designs
( lurusrnrctirin rll'liil[lD :-Arriilysis qf BIBD
- Analysis wlttr recovery inter-block infurrnat.ion
-- Yr.iuden 5r;tiarc:s -- l-artirre designs - Partially Balirrtcerl Incomplrrie Elocl: Desgius Arralysis oi'PBIBII - Ana.ysis with recovery of int':r-bloclt iulirrmatiirn - t.)piinrai:t;'of
dcsigris.
Orthtiguntl l,atirr Squlrcs: Onhogonal Latin
Sciurires -- Corrstruction
of olthogonul Lttil
Square - Congtruction pf orthc"gonal Latin Square using Partially Balanoed Designs.
'l'ext llouh:
I
Das pll.l.J trrir.l Giri. N.S. Dc:ign and Analysi5 t'i'Experimerrts (2'"r[itl). New Age Intenrational
(P) Ltd., l.,lciv Dellri. ( 1999). (C:ltilptcrs I --t ).
Itelerence Ilool,s:
l. f)csign iurd analysis of exp,:rirnents: Dortp.ltts C. Montgomery. :nt,n Wit.y antl Sons, Nerv
York.
,
!
..,,t{
t
rr, -,'rrrrrrls(0r - J_-l: l,rogranrrlilg
irr
C++-
IJri,cinies oI olrjcctcd*orierrted
tictl Cofnputing
r,ing: iasic concepts r.rr' (-)b.iectetl-oi-;enli.;,r
(O{)P) - Bt:rrclit ol'OOt'}S - Otrjcct-Oriented l-anguagcs -_,,\pi-:licarirrns oJ.OOp.
J. Iirtroduttir:n io C++: Stnple progranm -'l'he outpul olrerator - elharacters, sl ring litterrals anrj
1.
Pt'tlgrilirrroiting.
String leng:th- Cciinlrrent:; - Vari;rbles, Objects an<l tlreir rleclar.'atit:rrs .kir:,;r,,,r:,rrlr.ir,-rl lrj.,rrrtili.,:r ,;
Initialising in the dcclar.rtiorl - ('hairrcd nssigrrrrrcnl.s - Senricoh-rrrrrr - llrtigrarir style -"lirtqg.ra
types - Sirnple arithmetic operalors Operatcrl' precedence and assr-r<.:iativit'' - 'l i'Lr inuienterrr
;irid
decremcut operators -- Ci:utpounrl assignrnerrt expressicrns --' Ii11epcr,,r.r,:rttl,ro'..;rrii1 rrlilrr l1rii,
'fhe r-'lrar type.
-L Conditiorgl stateutenls antl irrleger types: Input - the y''statenrerrt - the iJ'.-. else statcmenr
Itclational opcrators -' Contpound statenrents - I(eyworcls Cornpouncl r:orr,liri,rirs r\
I,]oolea'
expressions - Nested conditi
srt'ilch stBlernent - the conclitional expre.ssiol operator
scope - Enumeration type conversion - Iteration aLrcl floating typl:;.
rslt/cstatentents--'I'lte statement -'I'lrcfor -slatemrnt-'I'he hrcult -.lalenler)t -.
The continue statement -The golo statement -'[he real numbfi.typcs - t],pe c(-lflversions.Round of error - The E-forrnat and floating point values Constanis, ,..r-iiill"s md olrjects.
4"the
-
Generating pscudo random numbers.
5. F-unctinns: Stantlard Cl library functions -- User definctl flnctions - 'I'e"ct <irivr:r:; I;rrnction
declarations antl deflnitions - Separate cnnrpilations
- l.ocal variables aud furrctir,rns, toil
functions -- Roolean lirtrctions I/C) hrncliorrs Passing by rcft:rcrrcc - [,as:sing by constant
reference :-elnline functions - Furrction scope Ovet loacling The inainQ and e:iiQ firncrions
Defiult argumenrs.
/r- ;\r'ray.s; Irrrtcessittg arrays '- Initializin[l an array -- Passirrg an ilrriq, to u {irnr:lirrrr 'l'lrr: lilrr::rr
s,.:itri:lt ttl.l.oritlrrtr .- ']'lre trLrhble .sort -lgor'lhrn 'I'hc l.lirrar.y scirrclr algoritlrrrr (_tsing arr;rys rvitlr
cnrrrlrr:rntiorr t,q)es -.]'ype definitions Multidirnerrsioiral arrays"
.
7. Pointers and rcfcrences: References - Pointers - Derivecl t),pes..Objer:t arrd [...,valrrrs Rcturning a rcferettces -- Arrays arrd pointers -'l'lte nerr'ol)erator .'I'ly: iclrlr r.]l)r:riiti)f - I,)"rr;arrrir;
arrays - L,lsing can,s7 rvillt point,srs - Arrays ol'poirrters anrl Jroirrt,--r:; [o a-rrgi.ri I,oBrf'ers t,.r
pointers .- Pointers to tirnctions NLIL. NLILL atul void -- irrinp.lr - r;r.riirrEs ttit t - rin nunrlr:r.
furrctions - Character functions - Defincd it <ct_vpx,J1> - ,,\rrav.s ulstriiltrs i't-t* r -strinl handliug
library.
8. Classes: 'Class declaration -'Constnrc'ters
- Constrrrctor initializ-ation list - Act:ess tl:ncli<lrrs Private nlember fi.rnctions - the copy coflstructer -- 'i'he class desftucttrr - ( lolstant objects Strectures - Pointers to Objects - Static data rnenrbe rc - static fiu:ction rnelnbcrs.
9. Overloading operators: Overlolding the assig,nmerlt operator - Tlrc //ri"s poinlcr Overload
arithmetic operators - OverloadinLl arithmctic assignment bpcrators -" Ovcrloading, thc relati<lnal
operators - Overloading the streiln operatofs -. Conversi<ln operators -- L)r'crft.iirqling l.ire ilcrement
aad decrernent operators - Overloading the subscript operator.
I0. A string cla's.r: the string cla.ss interface - Constructors imd destructr:r - T'hc r:opy constmctor The assignnlelil operator - The nddition operator - An append operator - Acccss functions
Cornparison opcrators - Streaur opcrators.
^II. Cornpos.itiou and inheritance: Composition --.Inlreritance - protcclacl class members -ovctriding-and dorninating irrherited members - private access versus pntlecte i access -- vitTuul
Iunr:tions aritl gtlymot'phisrn -.Virtual destructors -- Abstract basc classies - (.)bicr.:ti,:rj Oricntcrl
Ill:crgriu urn inF.
f-J'
$tre*rt: !./(): Slti'elrn r;las:;es - tlrt: io,r class - ios fbrnrat llags - fos state variables - t}rc istrcunt
utd oslreunr classcs - lJrtfonrratted input relaticlns - Uuforrnated orrtllut {i rrrctions .- Strearn
manipulators.
/J. I'emplates and iterators: Function templactes - Class templates -- C<tntainei' c:lassr.:s -.;i:lrclass
templates - Passing tcnrplatc classes to tenrplate pararneters -- ,a, t)lit;is tcriri:ilnfr: ii:i' linke,i lirts
Iterated classes.
/d. L,ibrnries: Standatrl C]*F library .- Proprietar), libraries
String stnu.rns
-
File processing
-
."-
Contcnts ryl'thc :.rtuxlarLl
f
hearlers
.'
Standard ternplate librtul,.
Awareness of any one of thc packages: (i) Ivlicrosott trxcet (ii) Sratistir:a (iii) SPSS (iv)
MINITAII (v) S t.
T'ext flooks:
1. Schuunr outline seies: Pntgramnting u'ith C'r{ , John IIahlturul, ,itr'G,rr*, lIitl, New York
15.
(1ee6).
2. Olleclcd Orientail Progrtnuning n,ilh g+-t. BulagurrLtn?trnr_yt 'futu llc'Grurr Mll,
New
Delhi(I?95).
III Serncstcr - 3.5: Practical II: Strrdenls are expccte(l to cle velop (''l-+ progi'arns rnrl to ir.!n on [)C
for all statistical teclrrriclues cliscusserl in 2n'l artcl 3"1 setrcstcrs. lt is also cxpcr:tccl that tlu. $ru(lcnrs Lrr.
{:.n.ili.".,ith
.'.'.,.--.
-r.r-
't
Irr-
e
'o
.,
u'.'1..
\l.
li,.
'i'
Buv.csial Anulysis (2,,r
Ed.I Springer,.r.1:3.5.6 and 3.s.7r,a
0., 4.8.3., 4.9., 4.10.,--{. f.*..pi
I i.), j f._"Lpi
+.+1.+.,
I
cals for papers 4.Zto 4,4
:
1
{:)i" ,.
l- (.),5rr:r"rrlirrns lLr:.scul.ch I:
l. ,r\tlvatltcrl topics irl l.,inear l'rograrnnring: 'I he revisccl sirrrpler rnt:thtit] - t)utliry.tlrepr.v alr6
its applications -_ Drral sinrplex rrrethotl - Sensitivity analysis-- l)rrrarrrctiir:
1.,1.t.r1r;rri1ririir11 (.lr:li
2'
3.
4.
5.
6,
7.
prograrurrring.
r.
[nteger Progmmnting; ComoIy's algoritlrnr lirr purc iirtr.gr,-r liirirai pir.rqiurrr: ii,,ir;r;r'.r'r;
r:rixt:ri
integer-continuoLts varjable algorithrn
Branclr
arrcl
bor-urr-l
rrrctlrocls
l-'rrrr
pr,rl1,11q11nj;.r1
irilr:;ir:i
proglamnring - Traveling salestnan prroblem Applicatiorrs of iutegei'"l,rrr.rglanriirinl;.
Deterrni4istic lnventor] IVlsders: 'I'he classical Economic order
Quantiiv tpr_lo) --'l"he nonzercr
lcad tiure - The L.oQ with shortages allorved .- production L,ot-size rlodel"
Probabilistic Inventory lVrodcls: A single period moder A lot size re-order point model
variable lead times - The irnporrance of selecting the right model.
simulation: Formulatirrg and implemenring a simulition model -. Jrp..i..u,ol clesign for
simulation - I{egenerative method of statistical analysis.
Network analysi.s: Terminology olnetrvorks - lvlaximal flow problem Shortest route problems
- Minimal spanning tree problerns - project management,
Decision fuialysis: Cltaracteri:itics of a clecision prohlcnr -- 'l'ernrinal tlecisirrrr bascrl op prior
inforntation - Decision trees - Sequential clcci-sions Infbrmatiorr acqrrisitir:n clecisions.
-
'I'ext Books:.r
l. Ithvindran Philips and Solberg. Operations R*.**.hr Principles antl practics. John Wiley ancl
Sr:rrs, Nerv York. ( I gB7).
.1. IIilL:r.!r.5:. autl l-,ietrerlnirn Ci.J, lntroduction to Operations l{eseir.rcl.r. lvlcC]rirrv ilill, Ncw yorl<.
( I !)e,5),
OP-2, Srrruiv:rl r\natvsis
I'
23.
Survivzrl tirnctiorts iurd htrzar,J ratcs -'l'ypcl; ol'censoring: 'l'1,pre I,'l'y1lc ll ,rir,i r.:r,r,i,)r11 1)l*'li ()l
censoring - Parametric modcl.s,
"t
Estintation: N'{axinrum likelihoocl -- lirrcar cr,rnrLrination r{'ortlr:r ;qlilri.,ri...j lJils r:rtrrer-.ir:ti
estinrator, IJN{vtiF. nnd Bayesian estimators .- I{egres::iorr Lrrotjcls.
Non-ltarametric mcthotls (one samptc): I.ife tables (recltrcetl iarnplr: rrrcr-lrrrrl : ,,\ctulrial
metlldd)
4.
-
Types
of lifd
tables
-
Product limit estimator -- I-lazard fi.rnction esrirnators
-
Robust estiruators (l--estimators, M-estimators, IJayes and eurpirical llai,es estirrrators).
Non-parantetric methods (twn sanrple): Ciehan test -- Maritel-Ffargizel tesr - 'l'arone-Ware:
class of tests
5.
6.
- Efron test.
Non-parametric rnethods (K sample): Generalisation Gehen test and fularrtcl-Hacnszel test,
Non-parametric regression: Cox proportional hazard nrodel (Conditional likelihood ancl
pemial likelihood - time dcpertdent cor,'ariates
- Estimat.iorr oI srrvival lirnctiol an<l
asyrnpto'tic propefi ies)
7. r\ccclcmtcd
8'
.
!).
(ilrrc rrrrrttcl.s: Lirrclr rarrk tcst -- l-cirst lj(.luat.c t."stinurtors_ Iv1 illcr cl;t.iruiitors .,
tluckly Jarnes estirnator - Koul-Susarla-Vztn ltyzirr estiurator.
Goqtlness of fit: Graphical nrethod (onersample and'K sarnplc) Ccneraliz-e6 l,iolrlogror,Strnirhr-'rv test - Generalised Cramer-Von Misei tcst.
Analysis of Conrpcting Risk Setup: T[re concept of competing risks Estirrration in the
exponential rnodcl.- Testing stochastic dorninance (Sign test Trhe Baga i- Deshpande- P{.oc har
test) - Llonrparison of trvo dependent competing tisks.
Dooks:
l. Ilupcrt C. N.liller. Sr:rvivrl r\nalysis. Jolrn Wiley & So:rs, hli:r,.r Yorli.
2. Deshpande. .1.V. , Gore A.P. ancl Strarrbhague A, Statistical l\nal,vsisj o1' rrorr-rutrlr iij I dilta,
'fext
o
Wilcy IJastenr (1995) (Clraprer l3).
I{efercncc I}ooks:
l. D. Collette. Modelling Strrvival Dal.a irr lvlerJical ltesearch, Chirrinirr & llall. [.qrrr1qn
2. Co>cp.R. and Oakes. r\nalysis of Survival Data. Chag[Hn and Flall. Lonclon
(1994.1.
l.
.
'I'lre a:ralu-t' iirid sources of tr:oriorriic .l*\tJi"1'v1,.. ci'ccr,rr.rrnic tlatir 1't'ilnts sai,'", - ct'uss-s(t.ti,i.'
1
Iroolutl) .lllu.r'ccs t;f rlar.ir - Acculacy ol'dala.
"
i,i*iesr Ilrgru.ssir-rrr tvtrrtrlel: lhc k variatc Linicar llcgrcssiou Modsl - Assurriprions -'()l.S cstinration
I'lti ctt*ti.ir"lii:nt iri'rlr:iurnrirrrtii:n -''l'csting siginiticencc of nrultiptc rcglc..:sion --'l'eltiing siurriticarrcc l-,
'l-csting
ri]l!i(::Jsirirr - 'l c:;ting ccluiility rrt'twri rugressitrn coct)lcicnts - '['cstiug linear rcsuicrion
-
[/i!1iiil
ibir irttrctioipiI iorrn of rrgrrs:iiol (lrr:trvcr:n lirrclr and loq lirruer rrlirussiorr) l'rcdittion (lvlcln prcdir:tion lirtiivitlu:tl l)ruJictir-,rr - Vali:u,';c tit'nrcalr pr(,(lictior - varaianuc ot'indiviilrral pri:diction ) -. l'he u'uiku
l.
hvl.rothesis tclrr;.
ft{ultiuolliueality uutl lilicrorrurnerosity: 'l'hc naturc ()f'[!luliicollirrcarity-- li:;iirtrari,!rr ir; Ihc prr:cnr,: r,f'
trlultir:r-rllinc:u'iry - listiruatir-ln in plr.:5cucc ot' "ltigh" but "lrrrlitltc,;t" Nlultii:ollirrcatitv - 'ilrcor"ciiu:tl
of urrrlticollinciuit'v - I)racticel c(,risequcncul; ol lvlullicr,llirie:ir:iiy ii-urgc i,:rriarrtui; ;rrd
ol ()l.!l estirnnrors - Wieler corrlitlcrrcc inturvals - "lnsiginifiulnt" t latios - n tugh l{r hut I'cu'
(:ortsLitlircrrr[s
uor'ariances
significarir t raritis
-
SErrsiritvityxrt'()l,S qstimaturs and thciir standald crr()r's to v?rxrll chrttrges in tiatu
of r"Llicuronunlcrosit)') -l I)etecriorr of lv{ulticotlirreariry - Itcnrcclial mcosrrrcs.
4. Ilttcr'oscetlosticity: 'l lru nitturu of Uctr;roscutlasstioity - Ol.S cstinration in thc prcscrrcu of'
Cc,nsctiucncjs
I'letr:roscc<lasricity -. 't"he
i.
6.
lnfihod oi GLS (dilt'crcnce between GLS and OLS) - Ctlnscclucnccs of using
OLS in thc presclcc of .Ilrtcroscsdasticity (OLS ostiulotiur allowing hcrsrosccdasticity - Ol-S r:stinration
disregarding heterosceilasdcitl,) - Dctection of lleterosccdnsricity (int'crrmal antl tbrnrirl mcthods) l{crr rcili:r I tncasurcs.
'l'rsdiiiorr:rl cconolnetric rrretlioilolrrgy: 'l'hc traditional viurv
of ccontltnctric Iuodclling (Avcruge
Ect)rrorriic ltcur-cssion (AEII.)) -'lypss of specitication errols - C-onsequences of spccilicotion rrrotlcls
(I-.liirlcrt-tuilg ald o.,,,srtitting a nrodul) -'l'csts of spcciticntion crrurs - Ilror$ of nre:tsu'enrelrt )
Altcr5:rtive ecorurnretric rnethoilologies: l,earncr's approach to nrxlel .\clecti()n - I{cndrv's aplrruuclr to
'?. Autritorrelatirrrr:
Nuturu til uutoqolrv-latiorr - ilrc Ol-S cstinratlon irt thc prcscocu of autrlcorrclatiorr 't'lte IJI-lJE cstirtrirt(,r iri tlie presencc qf autr,icorrelation
- Qonsctlucnccs ol using OJ.S irr thc prcsuncc of
sulr)ttolreliitiou (01,-S w(imetion alhr,rvirrg autocirrrelution - Ol,S esrirrration disregarding au()corrclarion) -
ilt
; ti::l ,i'
lriqhu-,r:rdcr tr,rtor:rrrrul:rtirin)
--
l{cnrudial nlu:r:-uru:s :
r\itlor'egt'ussive u()rtditi()nitl
lrcl,:rtricL:dlrst it:ity
lt. iitgrission on l)unrlny variables:
()
i'llc narurc ol rJurnrny variatrlcs - Ilcgr'cssion on orrc quantitativc
r';ti'ialil'c tvith oni: nr rirorc quali13tive variiilllc - I'estiug ibr sructtu'el statrility of rcgrcssion rnodels corr'r1i:itirrg two rr:Urcssions - lnlc:'lctir-lfi e.ft'ccts -'['hc usc of durrrnry variables in s;easonal rrnalvsis Picccu'ilic lirrtgr rcglcssion --'l'lrc trsc ofrlrrrttrlv vitt'inlllus in cirrtilriuirtg tintu :ir::its , r,*,' ,t, tirirrrrl ,l rt;r
.
Ilrr il1(ct'[)r'(.:tllti()rl ()l'rlullll].viir:iulrlcs rn surnilrrgulithnrtc rugrussion
Illorlcls rvillr rlirlrrrrrl rlrlitotltrl r':rr-i:rblts: I llrr lirrr'lrr Pr'ollrlrlrty rrrutlil (l.l'lv'l)
Prr)lrl(rur, il
Qtrcstionlrhlu villuc ol'l{' a..; a rnclsulc ()l'g(x)dnusri irf iit) - ApJrlications l.l'}N{. l. lhu l.rrgit Nttilcl l-:stinratiou of logit modcl . 3.
probit nodcl =- Logir vcrsus Probit - Comprring Logit and.Probir
"'lhc
cstirnittcs-'fhcn,alginal etTectofauilitchangcinllrevalrrcofarcgrcssur.4. l-1rc'lirl:itnrtxlcl.
10. I)yrranric fcorrornetric rnodel: Autoregrcssivc arld Disrrihutcd-Lag nrodcls: 'l'he role of "'l'ime" or
"[..ag" in l]uonourics -I'he tasorrs liir lags - llsitrnirtion tlf l)istributed-l,rg modcls (Ad IIoc cstirnution) -
I'lte Kuych ilpproash to disrr'itrutcd-l.ag rnodcls ('l'he rnctlian lag-'l'he mcan lug)- llarionulization ttf rhe
Koych nrodel (The adlrptive e?{pcctations model, the strrrck adiustmcnt or panial adlustinrcnt model) ('otrtltittlttitin uf ltilirptivc cxp\rctlrtir)ns und p:u'tiul arllrtstutr:ttt rrurtlr:ls - l:.rtint:ttion ol Autorcgt'ussivc
Inodt:ls .. 'l'he nrctliod ()f inslrurlruntirl variablcs - l)ctuctiilg ilutocorrclirtion in uutorcgrcssivc rnodcls
(I)urtrin L rcrt.) - 't'hc Alnr,.:n or l'}olinornial l)istrihured l.ag (PI)l ) - Causalitr in l:crrrronrics ( llre
Crangrr tc:;t).
11. Simrrltant$us-llqurtion lVlorlr:ls: l'hc nurulc of simultancous-cquation nrodels - '['hc sinrultancousc(luatiolt bias. - 'fhc identitication problcm'- Simultaneous-c(luatiorl nrcthods lApproachcs to ustirn:rtion Rc'uul'sivc tn(l(lu!s iln(l Ol.S - listinr:rtitrn ol'Just ldurtitlud l-iqrution ( lhe nrethod ol'll.S) - I'jstimation of
ovcridr-:ntilisd crlrrutirrn ('l'lru rtcthotl rrl'trvrr sirgc lerist stlurg'c (2 Sl.S))1.
,.
l),. .[:]+yesiarr h'ntltlurds in Ecorrprnqtrics; llayesiau analysis of the sinrple rcgressiolr model - 'I'lrc oasc of
diflirsc ;rrtirs _. Buycsian analyis of nrultiirle rcgrcssiou Irodcl - Ilayesiun anllyis of rcgrcssiou rrodcl with
liutototrclarril (rnrrs -- llaycsian inl'sl'cnUg irr systenr ot'cquations -- Bal,usiln nnalysis of simultarreousii(ltiiiti(ifl mOtlu:lii.
'l'c:i! Iitiolis:
i.
l.J:irnoriitr N. (jujarati. B;rsic iiconorrrctrics (3'd [ii.l.)
-?. (i.S. lvllddalu. liconornctrits. Nlc(irrrv-llill,
Mc(iraw-lIill lntcrnatiunal. Ncw York.
Ncrv York lnternation;rl srrrdcnt's cdition (lDlJ6).
liclel'errce 1|oillis r
l. Ii.t:lrcrr S PiruJyck and L]arrigf 1.. liubirrt'cld. Luotlorlutriu tr'loilull eu(l li:f,ojrolrlurrir l'')rcirit:,,
i\{c(irurvl IilI Interrraritlnal, N*.r york.
'J.
Kotirstiyiurrnis.
'1
lreory of I:corrttmcrrics (2"r
tld,).
N-lcMitlarr. h.lcrr, .r'orl< (1096)-
,(,
)3
,r-,*-"*",ra^, vcrs,s
arrd nr)rr rrri {llu!r1at i,,:iil ccrlranr
ic:;
-
ol'cquilibriurn _ l)artial nrarkct
cquilibnurn - (icncral
rrnc analvs
i.s_
eral tlrlice varillrlcs: Irr<iblrrrr rrl
arnrcs.^and
.r rrrrrli1.l,1,rihr,:i lirrir
intcgration _ l.ortnr I rr*r.gir*rl
lirrrt:tr,rr
"r,,t,,,,t.
Irl - Prtr-crtt vulLrt: ,,[. r.;t:ll llrrrr
t,,,
I)ynanrics ol'rnlrl<ct pricL:
liolurv
tlrchr;rticitl 1.],.:on0rnics
lcmctarv survcli 12,',r
(_1,,'
l::tl.;
lid.).
ir;ru-llill.
f.Je r.v
[lllrrl.Jni.lil,
Ncrv
cunstiuitictl lirruar. Inrsr;rrn utrrlt:r
rattcc Utrnstt:tincd
' \tlTl;tPhilips
4'
.nd Solherg, opcrations
Ru.sr:arch: Principi,:s
lirtul
l)t.rgr.ilnt\
",
r
z_ur
o ()tdur
norr-
unr-11y. s11yJ;-2,;1,y
arrr r)r,acrics. .rrrrrn wir,-.i ;rrrtt lirrns
i\rr:rr
Kambo N S' Mat,crnaticar prograrnuri,g
l'r:chnitlucs. East-west press. |Jer,r, r)crrri.
o
119g.1,y.
ir
,,t
g-1111111;,r,,,4,r1.
Nlr;(
I\.crrti,;,:
,.,,,,
I to./
t^
Ravindran Philips and Solberg,'()pernifrrs l].esearch: l)r'inciples arrtl. l'rlt.ti,.'r .l,,lrrr \\ ile'r
Sons. Nerv York. ( 1987).
4. Karnbo l.l.S. lr,tathematlcal I)r'ograrrrrning 'l'cchniqries. litrst-West ['rcss. I.ie.,v l)i.'llri. ( l rlj 1 r.
i.
..
\-
OP - {i. .(jtutisricrrl Quality Corrtlul
l. Statistical Process Control:
l.l
r
hrti'uducaioo to Control Chart:
clurrt -- Detection of clrrrnges.
l.l
-
Variation and the Corrlrol Chart
:
An auribute control
-
-
-
Controi
Behavior of varirrbles data Normal .distribution
(.ieneral
principles
charts.
olconlrol
I.-] {-'onirol Llhrrr lbr irttribrrtes: Charrs tbr llrrnltrer of Pieces Non(loutbnninE - Charrs ti;r
Percent Noucontixrning
Charts for rmnrber of t!onconlormiries - CfC curveJ f-or attribures
Contrnl chart printiples
i:harts lbr averages and ranges
-
ctiltl-,J cIralts.
1,,.1
'
{}rrrtr''til
{lhrrts l'rir varjabltls: lnilivi'luals
tjtaricllltLi lieviiiriuil uhirrt
-
Arrcrrge
(r'-
trar)
(.r) chart
-
ltational strhsroups _- Rnnqe 1l'l )r:harr
- har) i:lrart - lvlidrarrge (rtl)
chart'- lvlediarr (r
clr:irt - [::vtrluirtiorr of corrriol chrrtts.
i.5 Sp*r:iitl Coutrril Cliarts: Llurnulative Srun (lorrtrol Charts - 'l'he erip.o;lcptinllv rveighted
rrtovirlg svElage corltrol charts -'lvlodi{ied or Reject cOntroI lirnits lbr -r-har charts - Acceptance
control ctrrins.
2.
foltttrritls lbr'Quulity llnjrrovrnitrtt: (iraphical tr,tcttrotls tirr
J"
'l"cchniques - S.lpc,::ificlrit'rlr l.irnit:i.'fti[:r.lrrrr:us urrd
re llir-,.1
i)Iocr::;r { rrritr,.ii
QualiLy
tut:ltni(luc.l
r\rccptrurcc $.rmpling;
3.1 Single anrl double ottribute saurpling: Sarnplirrg risks-- Sampling.variations
.
sarni:ling plans.- Single'sampling
-
-
I'ypes
ol
Double sarnlrliqg plans.
Nluliiple attritrule srrnrpling phns: Item by itern sEcluential sarnpling plans
Cloup sequenlial plans - Derivati,rn of Marched Plans.
-1.3 A ttribrrte Samplitrg 'Iebles: ANSI i ASQC Z I .4 - I 981 . - 'l'he Dodge-Romig Systern - LQL
.J.2 Serluentirrl autl
-
irrdex systern.
3.'1 Special Attribute sarnpling proceddres: Corrtiluous sampling plans
plans - Clrain Sanrplirrg plan.
-
Skip-Lot sampling
'fext Iltxrk
l.
Ir,ittdern tttcfhods tbr clrrality control alrd inrproverrrent, Wadsworth, Stephens rnd (iodtiey. John
Wile-v and Sons ( 1986).
t]ooks:
StatisticalQuality Control. ll.L. Grant and IL.S. Leaven Worth. McGrarv Hill. New York. (1996).
[.Lcftirerrcc
L
{)l}- 7
i.
la,htstril'rl Statistics
tlurrlity ilri{I i{s rrierisurc: Quality rtrrd reliability
si1,,rnit rrir:l hr.rditk-,
nrrtl distr"illrrtions: Non-prrrtmretric rnethods
rlrtirl r'ttes,- !l tltisticlr I Pr.oues:i co ltr(') I
4.
The 'l'nguchi lvlerhodology -. 'l'he six
g_V,
2. Ilall
.i. ltelitbllity
-
Probahiliry phtting
-
Point nrrcl interval
I
rrtltl lt:itcs ol'irrtilure: lteliability C'lrallrcreritrirrions - ('()nritilrrt litilrrrc lrtc rrrr1dcl
-'Tiniiidependent fhilure l'ales - Cotnponent ftrilures and tuilrrre rrtr<lel.\ -- Iicpleccrr:erirs.
[,oads, Capacity antl Reliability: tteliability with single lorrding - H.'ctiaLritirv rrid ::lteti,
facrors
-
Repetitive loading -- Single lbilure modes & Cornbined tailure nrodes.
5. Relirrbiliiy trstirtg: Reliability enharrcemerrt procedures - Non-pararnetric nrethods testing - Accelerated life testing - constant tlilure rate estirnptes. '
_ 9*,t-lotgd
6.
I{etlurtdancy: Active'and stand by iecundancy - redundancy liiritations -. lvlultiple
rcdrrndarrt systems _ Re4untlancy allocation _ Redundancy irr corntrllex conliguration.
7. Ivhirrtuined systelnst Prevenrive ntaintenauce - Corrective rnaintenance - Repair: revealed
tailures - 'l'esting aud l.epair: unrevealecl tailures.
8. f'ailure interactions: Mru'kov analvsis - relinhilitv rvith strnd b.v svstL'nts rrrtrlticolnporlenr sysleru - availabi'licy.
I' System stfety analysis:
Product and equiprnent haz-iucls - l-lumarr efior - tvlethorls o[
rrrrllysis - Fault tree coflstruction - Direction evaluatiorr of lault rrees Fault tree evaluatir:n
cut
nby
sets,
'!'ext Urtols:
l.
lntrodtrctitln to reliiibility engineering: tl.E. Lewis, John Wiley anri Scyls. Nerv Yor-k. 2"'r E,l.
I
996
'
-\
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lj.
r\ci.,iar.ial i\,larhcrn:rtics -
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|,h,:i:Jtorttics
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litrte ti,^s li* 1t1ivc rtr.rtrlr.:l'*
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lirnctii-rrrs htr r.ctircd nrcnrbcrs Ilasic fiurctions
ot-active and rr:tircrl rn
'l'ext Iiook:
l. r\ctuarial lvlailrenratics. llnrvcrs N.i, (jr), Gcrtrcr II.{J, Ilicl<nrau
.1.C.. .Lrncs t-l zi an..t i.Jr:rihir.r I ,.
Strcicty oI Actrraries. ltasca. lllirroir. iot,l (('lrupturs
4. .s. (r. 7. l(). l,t. I 5. 16. rrrrr] lr]
I
)
\r.
IlilT\/r:q.--r,r' ()r c4I TClr.r
( ...t..,._.,- tra et-- )
F.5r:. ,St.atisLiqs - -rddltlon in t-he syllahue of Iv scrntllrter
chanqes ln tlrt': Tst S+rne. ter - +p.--roved - rJr'(lers issued .
-'
Gitrr'r.l- l, arrrl r,lrr.)rir. IC I / ,, 5FC'I'Ti\-
c'Jftt/505./9e (r)
CallcuL Ihlversity
P.O,
r
dL'te<l 5.9.02.
Rearl: 1) u.o. C.)rz'Jl/4'156/99 dated 3t/Lo/21.)1."
2\ l4.l rrrles of tn.:eLjn.r of qodrcl of Studl es ln SLat--ist,j
(rrr:) 5.'1<1 ,s|t 2.{t/1 /?o}2, and 1/5/2Oo2.
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t/t'/ ).oc'L "
c:s-:
a
9-lll3
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as Ist PaPer.
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'Ihe
(
Scherne
'I'he rneetincl of BoarrJ of Studles in
2A/7 /2002 , resolvecl to irrcltr'.Je two
in ttre .l.V ttr :;emesl-er.
2)
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E:l
o.9!.1!is.!r-cs
sLaLlstlcs (p G) lrelcl otr
a'lrlitirnal modules V anrl VI
1
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4.t
Strat--1st.icaI c-lenetics arrcl (-:IlnJ-ca1 tr-i.a-ls (O r'-1
A.0
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t-rr.tCt.lC<r.[ 1 I.I bi.rger] On 4 ,1 , 4. 2 arrci 4.3 .
4v
I
4
_!:h _I,trr-l u l.+
A 1
4. 2
4. 3
4.4
(3
)
2)
:
I AnalYsis (o P-2)
Statistlcal Deeision rtreirrf ' Sndi"Baye*I"rt nrt" l.Yl'if,.s
(o F-l0)
Applteci StoachasLlc trodel artd Til1re ser-i r:s
Ana lysJ.s (o r.'-t 1)
.surv1va
-':ractic'I
- IT1'llsetJ
on 4.1 t-o 4. 1,
Th. Boa r<J Of Strrtl J es ,- I s'r mor'l i Ei e<l .Ll're syI Ialrus c)f J q-i'..lloa
l'..sc Statlstlcs - (ie) Ir'rnl-r f and paDer 'l l- - rro chancles.
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if rr.:ii()a t itrrrrs ortly.
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helcl on
approved
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stucries trelc] on 2g/r/2002
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'
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it i..:1. I s l_lc:s
fetles of fering
_
Heart of
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.the'nepartrrent
Irrriversity
of CalJcut,
t};ntro I I er of Examlnd tlor) ,
rhiversi ty, fnformatlon &entres.
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s of rrre,.eLing of llbar.rj of S LurtieS llr ,: L;i LIst_.i c"iri ( f C: )
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Rear-f ; -1
3
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heif cJ
)Minures
or meeti.e of
Acbclernj.c
c.un"rlo;3i.1n3i.,' ,, .j.2,.,n:.
g&riEB
:
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h,,:.r
on. 20.2.2003 r reCor*iended: i:o,ravf se the Fract:icdl,Ir,r.1__or-o
,rf
tl . Sc S ta ti-s t ics ..-rs f 01 r O,i,G :
a) tr,:E6lqrir-rg t.}.e-paFqr -1 ,5 rracbical II oJ. .seme-5tir 3 anct.
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cl.l sc r: s s ion anrl r a:cto l ve;r] t tre., q] 1
ovrlncj,
-f
l,r:<: t';rrt-ruqh nurr,Lxjr: or
are not ;:rv.:i la b-i *r -ir1
sen'e c€dtr.es for corrdue.t.ir.:E."ornputrer--e
the practic;lr alxarr,i.at-io,l,
s t-uden t.s .:re a-1-lo'.'r;-i t,o Usr: Sclelt.if jc qr(llcuLaLt.ir^
s fr.r_r. r:! ,.
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ii
Fr'rcticar r r:r 2nc] s.nruster (t1pe.r 2.s pfac'Ljcal r),l,ur:,j(rs
for the practlcal e;iamjr:al-1on.. fqf r
..
Fcrp€r 3.5 pr.ilticat II ar c_ basecl on
Faper 3.1 , :
t:uitivariaFe Ar,aly.sis
F aper 3 . 2
;
o,f ' samplr brrr*y t-iegions
o
F.aper
t-
Fap.=
3.3
r 3.4
:
^p611;sis
;
r-,resign and An6]ysisl
of
trogfalurr-lnq J-n,c
hnd,
[xpegi.me.nts
Stat-tstjca-r
,.
Conrprrl_ln€r
,
:
I'low..rver bhe internal c::arriiIatjon'for tlre
[,<]F€.rs .].1r. ar-rrl
J-+,:
iPro-i.ot tfup.'a 4.5 ) 1.r .tlie aLt-r'senres!ar: ir- ls
rtlsrrl ','r:cl l-haL the Frojrc-t_ mb.y, t:e, df resaarch (theor=-tic.t_L )
r-rr: r-:f Irrar-lt-ir:-r I natrrr:i_ .t.:, i ii uf j-ndivlcuall.i.
Eacir stur_, - rri
ha5 1i-- srtl.trri ti a .retr'or:t cr,-, Lirc rvofk clone by l-rtmlrer aL L16:
,=nc'! of 4th -qerne:gt.:r.
b) Recarc'l-inqr.the
(coutd. . -:i
)
5
) orclrrrs
'l't.i
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I rr
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r;i,i'l;'(l
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/
lll.?
.1,-t
/,'
C t )abe
Riries:
. rvith trvr.l :jc.rnostcr" iir ,.li1r-r,.: i.cllr,
nstruction eacli day undei
:_day
i_:ach sclnestcr
rr..l ;;;;
the 90 re.gular instructioiial ,.jai,s,
orking da_vsj
naticn
ion.
(Expected 9C worki:,g
rja;vs)
exalTi
.
m
;?
i,i. :i *pr
woi.king davs)
ation
!on.
er (Expectecj 9ij rvo;-i<inl_r
exant
,1i1,,,.j)
]]
is
sulject w,ilj be ,l,i:tidt?,.i b:, ii,e
iesDective
pailam
fl-rr
i_:f
firtt
v,,orh lerai.
s*neste:. an.j 4 thecr;, p
iri rach sei:oester:
Vivir_,,,oce
will
li
d
a
ir>n
be Conc= i,r t."\,o
F?.ris.
li
)-.
\1
\
(7,
r
.:
,1i11?i:r:ffi,:J""0 of the\#"''.nt
and the Departmenrar
coordi, tor for
There shail be provir;ion
fbr grievance redressar at
Ievel of teacher cr
consisting of the H
concerned: Third:
college council no
third level of commi
at the University
r _ pG Board of
Controller
.
.
Commitree.
of Exa
(.ollcgc/ l)cpartlncn
publication of r..uit,
on such decision sha
one week and deci.si
Normalization of cont
there is inflution
proponionatery
oi:
irthe
Icd rvithin onc wcck ol'
thc
e done by the University
when
,Hlf,J:1.;rj.,:i,#,*t:
le valuation for the semester_
5.
Exlcrnal ev:ltrration of proiect
ll.crrorr: .r.tr,. ......r.._..,
two exte
semester
6
Pass
tions will be conducted
and
Chairman).
e of each semester will be
e respective semesters.
The
am of teachers nominated
by
.. .isscrtation
isscrtati,, wiil
will bc d,rrc
dorrc bv
by
(external) at the end
of 4i,
ll be as follows.
requircmcnt: The
1.,;155 minimurn lilr cach paper
ivill ba 40%. 'fherc will
for intei,ral
bc
un.f no provision lbr
ilTlprovetnent.
"rniruiion
separate minimurn
rro
tt
N
Classifi cation of Results
:
80 oh and above
600% and above and below g0%
50% and abore and bElow60%
II Class
III Class
8. Ranking:
9.
Onty ttose c-andi
minimrrm.ori^.| .,,;ll
,_ ranking
^- _^ta , fbr
will L^
be cr,nsidered
on the basis of totar
;T,?IJff::iod
Promotion to higher semeriter:
whose
has been
higher t.rn.*Zr. Students
;il;;
;m:U:..*ui
wit h subsequent
*,.i,"3ili,i#f,l
hfJ:ffi
;ilii
l0' Supplementary examinati.n of failed
candidates: Candidates who have
tailed in
semester examination, can
appear
::il::Hl,lllo.r,r.
ll:
nimum required attendance (or
ll be eligible for. permitting to
cond
who
tr,. sem.rte.-arong
nce within the
rnarks,.H#?ii
the
for the thiled papers of a particular
r.r.rr., along with
rrvc such srppremen,urv'.n"n.es ( :onsecutivery)
wiil be given in
*h
l,l:
'
_ Pirpcr'
l)robabilitv;i
Measure and
a
i
1.3:
lirt crrr:r
I
l,,xlcrrr:tl
I
ol:tl
i :tt
80
100
20
80
100
Distrlbution
ffit&m...*
z.z: parametrliEtirutinn
z.g: restEilTsGm;t hi,
?.+: StochasticF.ocesses
l0
n
2,5z,.,PrasticalI
3,5: Practical II
2.2 and 2,3
inCr-r-andffi
100
80
l(x)
t20
t00
.s80
100
4.3: Option II
4.4: Option lll
4.5: Practiiafitl
120
Viva-voce
arO-
Totat for IV
580
r00
tt*Tlil;1L:.n.|#ll
__1
papers
rv. c'orrege / Departrne.t
in riemester
1. Econometric Methods
2.
3.
4.2: Opcrations ltesearch I (OI) _
l)
4.3: Econometric Mod:ls (Op _ j)
4.4: Mathematical Econornics (Op _
1)
4.5; pra-ctical III (Based on 4.2
and 4.-j)
Statistical et,ality Cont[ir,abp"roti,ns
Research.
r+.2: (Jperations
Research I (Op _ l)
4.3: Operations Resear,.:h II (Op _
5)
.1.4:
.1._5:
Statistictrl erutlirr, ( ,()ntt()l (( )1,
[)rircticirl III (l]asr., lon.1.1. l. i
Business and Industrial
Statl: tics.
4.2: Operations Researr h (Op _
I)
4.3: Indr-rst.lur staiisii..
_ nl
.1..1: Statistical
,ontrol (Op
eualir-v (
4.5: practical III (Baser on 4.1. _1.-t 7\ _1._t)
ancj
Actuarial Science.
4.2: Sun,ival Analysis rCp _
4.3: Actuarial Matiremarics (Op _
I
S,1
4.4: Actuarial Mathemarics (Op _
Il
4.5: practical tII (Basecl +.:. .1. 9)
an<i -l.l).
I
io,
4.
lt
tulrl t.-l)
lt
*
j
:lpq
can olfer
I
r.rrrr-'
o1
tirc,
I
t
I
r-;,
Semester- pnper l. l - probairitit-Wu,-,
1' Sets and classes of events: The algebra of events Fields and o-flcld-s
ckls:,ri-ure nls
2' Random variable: Functit'ns and inverse
lirnctions
-
variables.
3
'rrriablcs lirrirs )1.r.irr(i, irj
properrics Discr,rtc rrr.r.,irr.li-.rirrr
ranciorn
proba riritr, lreasLri'c and
erernentar\
abilitl' spacc Inducccl.prohabilitv spLrcc ()rlrc' rrrc.sLr.,,.\ ((
r(..ci...ii,..]ir
,
- Crtrirlitiorrlrl prol-xtbilitt. rr.tcasurc (,gtrrrtirrS l1)Cits1i.r. i r,ijt.,!rrr.
4'
::'l:t ,riii],l"'l
,,,,,, c.rcrncnrarr pr()pcrries r)ct, ,rr1rr, . , ;, ,,
tion theorern) - Distrihrrrion t ,.r,., .,. ,,. )
'
n.
7'
8'
Characteristic function and rnoment. _
,n,r.n,
problern.
convergence of random variables:
converyence in probabilitr, - (-.n,,erse.'rce
,lrr,rs1
"' \ \/r !
surely - convergence in disrritrtrtiol ,. (',.,nue.uenc.,
in ,.,,i ,ir;;;'"'
Convergcncc of distribtrlirlrt litrtcli.rr: wcuk
urrd c.rrrplcte e()r)\er,!eree ilr.il, ,,
convergence. theorem
I elly-Bra' lenttna - Hellv-Brav theorern c .rrr erlrcr(.r...
distribution firnctions ancl cl,,r*rc'tcririi. ti,,,,.,;,,,,,.
.,iuiin,,i,, rlrc.rr.rrr (clirt.r..r ,.(r i i,r\,,r,.\.1
Irrdcpcndencc: Indepcrrclertr.r: ol. cvcnls (.lass
rrl. irrtlcltcrrrlcnt c\clti rlrrl ir;,1r.Iq.11,.1.,1,,
classes - Indcpendence of nr,rrlorrr l,trrilrltics
Kolrrrogorrrr ()-I ltrrr Ilor.cl s (r- i t.r.rrer.tlrr
rov s rnequalitv apd il.s. c{)p\ qr"s(_,pce
rr ol large nrrnrbers (iirl elrse h.itirrteirrrr ,;
Kolmogoror,, SLt,N fbr iitl crsc
rrn - Liapnov's tbrrn _ l_indeberu_l,rllt,r
thi.-or,,nr
I
9.
Text Book:
l' B'R' Bhat' Modern Probabil ty 1'heory'(3''r Ed.). New Age
l)Lrblicarions (l()(,(i)
I
Semes-t-er- Paper
l
l. 2 - Measurc and lntegration
Measurablc Fttnctittns: Nl 'ltstrrltblc sets
\lclrstrnrblc lrrrrcti.rrs lrrrtl rlrcir i ,,11;ir,11;11;1,r1
Intost ev,cry rvlrcrc _ ('harues,
ntegrals - The irrtegral of non_neeirri'e ,lrrer.trlrrl
ntone Conver-qcnce l-heorc.rn _ I.irt.,us
[-enrn,lir ._
Properties of integral.
4' I,tegmblc [urrctions: Intcgrablc rcal valucd lurrclious
Ihc pt-rsirivity arrcl lrrcarirl bt rlrc
integral - The Lebesgue Dirninatecl con'crgcncc
Thc't,rcrrr Irrcunrls rv,lrielr rle'r.rrtj .. .,
parameter.
Spaces - the L, Spaccs _ lloider.s tnct;rrirlirr
Thertrem .- The spacc I .,
L,, - C'ont ergencc irr t,easure _ ,\l,rtrsr
t-r.riirrrr
Decornposition rheorem
Theorem.
-
r
he
8'
^
9'
Caratheodory Extension theorem
2'
Rana
*r0",-*,1111,"H::T,l'':lTn."L:',;:ll]..,"
Generation of ivleasures: l leasures on al-uebra
ol sets
-
I he e\tensiolr tri.
- 'lI-ebesgtre- and I.c,hes-{ruc_\riclt.jes
.,,.1]]f.,,j:1,1.ll]
,rcilslr.r,
r
ir,:
nreAsulc
Product mexsures: Rectang le's he procluct
lv1"ur,.,ri]il'l.,corenr Scctions I lle \
l()r((,.(
Class Lemma - Tonelli,s Theorem _ Fubini.s
Theorem.
Text Book:
l' Robert G' Bartle. The Elemerrts of Intesration. John wilei'arrd
Sons. Ne*, \.ork.
Reference Books:
l. Aliprantis C.D. and Burkinshaw O. principles ot.Real Analvsis
(.1,., Ecl.). Acuclcrpic t,r.t,-ss
( 1 ee8)
I'K'
Introcltrction to Nlciisrrrc rrrtl Irrrcrr:rlion Niu-osrr.
\crv
I)r,llri
- 6'-
ln(l cxistcncc o,.thc
es and important
ir)tcgral A
theorems
__
ncccssary and
First ,r"nn urtu"
ge of variable.
ded functions with finite limits
of integration
_
ma functions.
Se convergence _ Uniform
cont,ergence on an
perties of uniformly convergent
sequences and
rier series for even and odd functions _
Half range
serres.
6. Metric space:
T"., J:ilfleteness
-
_
Defrnitions and
Open and closed sets
,.exarnples
Continuity arrtl unitbnn
continuitf
,t;r:.n};[,,i'i1,j"r',na
Arora
(leee):
I-Corpr.,n.ss and
.
2'
3'
T.M. Apostole. Mathernaticl
l Analysis. Narosa
Rudin'
w.
(lJfrT*tt
principres
c'D'
Convergence and
connecredness.
Mathemaricar Analysis (2,,.r
Reference Books:
I
_
Ed.). New Age
( I 9g5).
of Matrrematicar Anarysis. Mccraw-Hir
(r976)
and Burkinrhaw
o'
Principles
of
Rear Anarysis (3.,r Ed.), Academic press
bution _ Distribution
f variates _ Marginal
ents _ Charlcterisric
Applcations (2*r Ed.). Wiley
Eastern (19g9),
Introduction ro the rheory of
Statistics (3,,r Ed.).
v)
Wiley and Sons. (Chapter 2).
Theory and Mathematicai
Statistics. Wiley
5.)
e advanced theory of Statistics.
_
Vol. l.
5, I 5).
iutc stutistical analysis (",,,r
cd.). John Wilcy and
t
t
1.5: Linear Models
1.
2.
3.
4.
5.
6,
7.
8.
,-\
(v
Vector spaces: Vector sp rces and subspaces
Inner products.
-
Bases and dimensions
-
Linear equations
-
Matrices and linear equarions: Matrices and matrix algebra - Systems of linear equations
- The inverse of square matrix - Determinants - Systems of linear equations - Genearalised
inverse of a matrix - Matri;l representation of vector spaces. bases etc. - Idempotent matrices
-
Kronecker product and Hadmard product.
Matrix norms: Norms or1 vector spaces - Norms on spaces of matrices - Propenies of
operator norrns - Matrix I rnctions detined - Banach Lemma (criterion for invertibility) -
Stability of algorithm.
Eigen Values and Eigen Vectors: Eigenvalues and eigen vectors - Important properties of
eigen values - Eigen values and norms - Polynomials in a matrix - Diagonizable matrices.
Jordan canonical form arrd applications: Nilpotent matrices - Jordan canonical form Applications.
Symmctric nnrl hcrntitittrr tttnlricts: Scltur's urritury triurrgulurizutiorr tlrcorcrrr Rcul
quadratic forms - Hermitii n fbrms - Reduction to diagonal form - Positive-definite forms
and matrices - The signature of quadratic form - Simutaneous reduction of pair of forms
Eigen values and Rayleigh,.luotient - Courant-Fisher min-max theorem.
Lincar Programming'Pr,rblem: Craphic solution - Sirnplex merhocl (Stantiard lbrrn
Duulity Slrtck and surplu:; vuriublc artilicial vuriablc Big M urcthod) -'l'rursportatiolrproblern - Assignment problern - Traveling sales man problem.
Game theory: Matrix gamcs - reducible to 2x2 matrix - graphical solutions
games in to LPp.
-
Conversion
of
Text Bools:
l. C.R. Rao. Linear Statistical Inference and its applications (2'n Ed.). Wiley Eastern (1989)
(Chapter I).
2. Lewis D.w. , Matrix Theory . Allied Publishers, New Delhi. (Chapters r - 6).
3. Operations Research . Hamcty A. Taha. Mac Millen Publishing Company, New York. (part I.
Chapter 2,3, 4.1 to 4.4, 5 and Section I I .4).
1. Sampling and sampling
ciistribu tii{i/ Population and sample - Distribution of si
Statistics and sarnpling distribution - Sample moments
- Sample mean and varia'
Sampling fiom normal disr ributions - t, F and 12 distributions (central and non-centri
Distribution of Quadratic fcrms - Order statistics (distributions of functions of orde, starisr
2.
asymptotic distribution (asymptotic distribution of sample quantiles asymprotr
distribution of extreme value statistic) - Application of t, F and
12 ( testing in normal
distribution) - large sample lcsts (standarcl error - normal tests - test of goodness of fit).
12
Gauss Markov linear model: Gauss-Markov linear model Estimabiilty of param.i.., Gauss-Markov theorem - Estimation of o"2- Analysis of variance of one way, two way, rwo
way with interaction - Anr lysis of covariance (one-way and two-way with single auxiliary
variable).
3. Linear regression
analysis: Linear regression models - Least Squares Estirnation ol'Least Squarc I:stirnittcs - [tstirnation tll'o..? - Orotltogorral Strtrcttrrc in thc
Design Matri.r - Generalis:d Least Squares -'l'he [.'-test tbr linear regression
- Multiple
Correlation Coellicient - .joodness of tlt test - Analysis of residuals (Definition and
properties of residuals - Re:;idual ptots Statistical tests based on residuals partial residual
plots - Transforrned residuais Trrnsfbrnirrg thc data.
Polynomial regression (sirrgle explanatory variable): Fitting of polynomial (Least square
theory) - Problems of ill-conditioning - Choosing the degree - Fitting of orthogonal
Properties
4.
polynomial (General Statist cal l)ropc'r-tics
-
(lenerating orthogonal polynomials
least squares).
-
Weighted
Text Books:
I' C.R. Rao. 1-inci.rr Stutisticrrl lrrlL'rurrec urrtl its Applcutions (2'-r Ld.). Wilcy Lastcr.n (19g9),
New Delhi. (Section 3b.).
2. D.D. Joshi. Linear Estimati rn and Design of Experiments. wiley Eastern ( )
3. Seber G,A.F. Linear Regression Analysis. John Wiley and Sons. (Chapter 3 (upro 3.6 only).
6.6).
4. Sir Maurice Kendall and Alan Stuart. 'fhe advanced theorv of Statistics. Vol. L
5.
Distribution Theory. (4'r'Ed t(1977) (Chapters 10. I l, l4).
Rohatgi V.K. An introducrion to Probability Theory and Mathematical Statistics. Wilev
Eastern. New Delhi(1990). Chapters 2. 4 and 5.)
Reference Books:
1.
ll
Kleinbaurn, Kupper, Muller and Nizam. Applied regression analysis and other multivariable
methods. Duxbury Press. Nc,v York. (lqq8).
Scnrcstcr- P:rpcr 2.2: Irrr.:rnrcr ric csliuratiorr:
I' Principles of Data Redtrrtion: Sufficient statistic - Sufficicncy principlc Minimal
sufllcient statistics - Ancillnry statistics - Sufilcient, ancillary and compiete statistics
Likelihood fi.rnction - Likelilr.od principlc Thc invariarrcc principrc
2. Minimum variance unbiast'd estimation: Unbiasedness - Best Linear Unbiased estimator Cramer-Rao lnequality and its applications - Rao-Blackwell theorem
- Lehmann-Scheffe
theorem - A necessary and srrfficient condition fbr MVUE.
3. Simultaneous estimation ol'severat parameters: Matrix optirnality crirerion - Ellipsoid ol
concentration - Klebenov- -innik-Rukin Theorem
- Cramer-Rao Inequality - A brief
discussion of M, D, T and E )ptimality.
4. Asymptotic properties of r:stimators: Consistencv - Method of moments - Method of
percentiles - Choosing betr"cc'n consistent estirnators - Consistent Asyrnptoticalty Normal
5.
6'
(CAN) Estimators.
Method of maximum likelihood (MLE): Detinition MLE in exponential family and
Cramer farnily - Cramer-Hu:rur Bazar Theorem - Multinomial with cell properties
depending
on a parilmeter - Solution of likelihood equation Asyrnptotically most efficient
esrimaror.
Interval estimfltion: Defirrition - Shortest expected length tonfidence intcrval I-argc
samplc confltlcncc intcrval: []rtbiitsccl cottllclcncc intcrvltls 13aycsiun lnd lritltrcill
intervals.
Text Books
l. B.K. Kale (1999): A first course on paramerric inference; Narosa publishing House, Nerv
Delhi. (Chapters 3. 4. 5. 6. 7 t0)
2' Ceorge Casella and Roger L t3erger ( 1990): Statistical Intbrence: Wadsworth and Brooks.
Pacitlc Grove. Calitbrnia (Chapter 6).
Reference Books:
l.
3.
E.L. Lehmann : Theory ot'point Estimation
M.T. wasan (1970) : Paramerric Estimation: Mccrarv FIill. Nerv york.
I hypothesi.s:
tests
_ invariant
.rat.io
tesrs
_ Bayesian tests _
Union-
er function _ Most powerful
tests
bin Theor.em) U"Ui*"j'_?
_ Similar rests _ I_o.olfy-rlri
_
firndamental ideas
pro pert ies
"
90):
of
seor
or,";;;###:Tr"r
j
stimation
sampring _
;ii;. i;:,,,fjff :: liXi il;Ji:
rs
Statistical Inference;
Wadsworth and Brooks,
tatistics.
l.
and Mathematicat Statistics.
wiley
'1'0.;n*"
E.L.
Lehmann :
Theory ol.point Estimation
2.4:. Stochastic processes:
l.
Introduct.
corrcept
,.oaaaraa.'ot"
ol
;ttlchastic process
-
e.xzunplc
-
rNop.ocesses
o
specification of. stochastic
_ l.he transition
probability
ur tr
trans it io n pro babit
iiie"svs
(amples -
.Il'jilg
models
rr
Distribution of N1t; _
1;rn;1
(WM/I,
WIWC and eueing
sysrem
ystem and clbsed
system) _ iyr,.,
_
WC/l
time
l.
-
(Bro
moti
S.M. Ross: Introduction
to prr,babi
Asia pra-Lir.,rcr*;;;;
R.r.r;"j;X,.dhi:
Gambler's ruin
ard
geometric
models (6'h
Ed.) (,.?nl).Academic press
,.',';;,,;'n'
i
stochas,ri-p;;;,:,.^i.f[:i;::f"T":". 7 to .s),, l],i'i'ol, .' and Harcourt
,
7
..4
3' S' Karlin
TayJor: Firsr course in.Stochrrsric
4' w' Fe'cr:""0
processes.
An ly'
introduciion
to'r,roilt;,i,r,r,.o.y urj-it.'ojpti.otions
vor.r.
't'.t"",fr'.'::,I*,,...?,?:r,if,;.IT::ffr,,';,,..r.:::;;r,,:ff:flui,l nor... 2.r to 2 3
and Vor.2.
Non-prosrarnmabre
------7
- l-t -
III -
3.3: Design and analysis of Experiments
Concepts of Experiments: Design of Experiments and collection of clata Experiments,
their design and ana]ysis - I'hree principles of Design of Experiments
Experimental error
and interpretation of data - Contrasts - Models and analysis of variance Analysis of
onetwo way and three wai classified data - Orthogonal and non-orthogonal data.
YaY,
Complete Bio_ck Designs: Completely RandomizJd Design Randomized Block Design
Latin Square Design - Method of analysis of experimentJ with missing observations (ngO
and LSD).
Factorial Experiments: t'actorial experiments and varietal trials Factorial experiments
with factors at two levels - l?inite fields anc design of experiments Crouping for interaction
contrasts - Counfounding - Counfounding in more than two blocks
- Experiments with
factors at three levels each - General method of construction of counfounded factorials
Maximum number of factors to save interaction up to a given order for a given block size
Analysis of factorial experirrrents - Fractional factorials.
Asymmetrical factorial ex;rcriments and split-plot designs: Asymmetrical factorial design
- Counfounded asymmetri,:al factorial design - Constiuction of balanced counfoundid
asymmetrical factorials - Construction of asymmetrical factorial vx22 in 2v plot blocks
Analysis of balanced counfc,unded asymmetrical factorials Split-plot designs Analysis of
Split-plot designs.
Incomplete block designs: Incomplete block designs Balanced Incomplete Block Designs
- Construction of BIBD - Analysis of BIBD - Analysis with recovery inter-block informatjon
- Youden squares - Latti,:e designs - Partially Balanced Incomptete Block Desgins Analysis of PBIBD - Ana.ysis with recovery of inter-block inforrnation
- Optimaiity of
Semester -
1.
2.
3.
4-
5.
6.
designs.
ofthogonal Latin Squarei: Orthogonal Latin
-
Squares
Construction of orthogonal Latin
Square - Construction of ortlrogonalLatin Square using Partially Balanced Designs.
Text Book
I'
Das M'N and Giri. N.S. De:.ign and Analysis of Experiments (2d Ed). New Age International
(P) Ltd., Nerv Delhi. ( 1999). (Chaprers I 6).
Reference Books:
l. Design and analysis of exp,:riments: Douglas C. Montgomery. John Wiley and Sons, New
York.
,
t
stical Computing
ming: Basic concepts of
Objected-OrientpJ
t-Oriented Languages _ Applications of OOp.
output operator _ characters, string litterals and
nd their declarations _ Keywards and Identifiers _
Inlcnts - Scmicolurnn _ I)rogram style _ lnteger
precedence and associativity _ The increment
;d
expressions - Integer overflow and under flow _
3.
Scope
ts and inleger types: Inpu
Compound statements- K
onditionals - The swilch st
-
e/se statement _
ns_A
Boolean
ssion operatoi _
Enumeration type - integer type conversio
statements - The tlo ... iiit, statement - The
lor statement - The break statement
The continue $atement The goto statement The real
number types type conversions
-
4' The while
Round
of error
-
The E-formai and floating point values
Generating pseudo random numbers.
-
constants,
-
u*iutl.s
-
and objects.
5. Functions: Standard_ C library function
declarations and defin-itions
- Separate
functions - Boolean firnctions itO n,
reference - Inline functions Function scope _
Default arguments.
ion
oid
anr
s_
6.
array to a lunctiorr _ Thc lincar
h algorithur Using arrays wirh
7.
ypes
rd pointers - The new operator
-
_
Object and L_values _
The delete operator
- Dynamic
Arrays of pointers and pointers to arrays pointers to
- NaL, NULL and void - strings - strings tio cin number
Defined in <ctype.h> - Anays of strings ihe c-string handring
-
ers
library.
-
8' classes: class declaration - Constructers
e
10'
:
-
Constructor initialization list - Access functions
- The class destructor _ Constant objects _
rs - static function members.
nment operator _ The r/rr3' pointer _ Overload
ignment operators - Overloading rhe relational
nversion operators _ Overloading the increment
TffirtJffi
or
Programming. .
12' Stream UO: Stream classes
atd ostream classes
manipulators.
13' Templates and
-
-
destructor
-
The copy constructor
An append operator
-
-
Access functions _
- Inheritance - proleclerl class members _
private access versus protectecl access _ vinual
ors - Abstract base classes - Objected Oriented
- the r:os class - r'os format flags - ios state variables - the istream
Unformatted input relations - Uniormated output functions
Stream
iterators: Function templactes -
-
- Container classes - Subclass
class template for linked lists -
Class templates
templates.- Passing template classes to template parameters
-
A
Iterated classes.
1r'. Libraries: Standard C++ library
- Proprietary libraries - Contents of the standard C headers _
String streams - File processing Standard template library.
Awareness of any one of the packages: (i) Microsoft Excel (ii)
Statistica (iii) SpSS (iv)
MIMTAB (v) S+.
Text Books:
1' Schaums ouiline seies: Programming with C#, John Hubbortl, McGraw Hill, New york
15.
(1ee6).
2.
Ohiected Orienlcd Pntgronuning with C++. Buluguruswumy, Trilu McGruw
Hitt, New
Delhi(I9eS).
III Semester - 3.5: Practical II: Students are expected to develop C+ programs and to run on pC
for all statistical techniques discussed in 2nd and 3Jsemesters. It is also e*pecied
that the
t^mrlt.?
rr/rfh
.r,rt.
^...
.C.l-
students are
_iJ
,q_
Bayesian Analysis (2,d
Ed,1
Springer,.r.1:3.5.6 and 3.s.)), +
1"*rpt i.i.i.,
0., 4.9.3., 4.9., 4.10.,
4.r i.), j
(.;;;;;
cticals for papers 4.2 to
4.4
OP
l'
- l. Operations Rescarch I:
Advanced topics in Linear Programming: 'l'he revised
sirnplex method Dualiry rheory and
its applications - Dual simplex methocl - Slensitivity unutri, paramerric programming - Goal
progriutrrning.
model
- A lot size re_order
right model.
a simulation model
point model _
e
analysis.
-
Experimental design for
Maximal flow problem _ Shortest route problems
nagement.
ion problem
ions
-
- Terminal decision based on prior
Information acquisition decisions.
Text Books:
I' Ravindran Philips.-and-Solberg, operations Research: Principles and practics.
John wiley and
Sons. New york. (19g7).
2' Hiller F'S' and Lieberrnan G.J. lntroduction to operarions llesearch. McGraw
Hill. New york.
(r ees).
OP-2. Suwival Analysis
I'
2'
3'
,
+'
5'
6'
7'
8'
9'
_
Survival tunctions and hazard rates - Types of censoring:
Type I, Type
censoring - parametric models.
Estimation: Maximum likelihood
and random types
of
linear combination of order statistics.- Bias corrected
estimator, UMVUE and Bayesian estimators
- Regression models.
Non-parametric methods (one sample): r-ire tiures
lieauceo sample method - Actuarial
method) - Types of life tables Product limit
estimator - Hazard function estimators
M-estimators, Bayes and empirical Bayes estimators).
sample): Gehan test - Mantel-Hanszel test Tarone-Ware
-
Non-parametric methods (K sample): Generalisation
Gehen test and Mantel-Haenszel test.
Non-parametric regression: coi proportional hazard,
model (conditional likelihood and
partial likelihood
- time dependent covariates - Estimation of survival function and
asymprotic
properties)
Accclcntcd tirttc rttodcts: Littear rurk lcst Least square
estirnators- Miller estimitors
Buckly
James estimator
- Kour-Susarra-van
-
Ryzin estimator.
Goodness of fit: Graphical method
lone sample and K sample) - Generalized KolmogrovSimirnov test - Generalised Cramer-Von Misei test.
Analysis of Competing Risk Setup: The concept of
competing risks - Estimation in the
exponential model- Testing stochastic dorninance
isign t.rt Thi Bagai-Deshpande-Kochar
test)
-
Text Books:
l'
2'
-
Il
Comparison of two dependent competing risks.
-
-
Rupen G. Miller. Survival Analysis. John wirey &
Sons, New york.
Deshpande' J'v. , Gore A.P' and Shanbhague A.
staiist;cat Analysis of non-normal data.
Wiley Eastern (1995) (Chapter l3).
Reference Books:
l' D' Collette. Modelling Surr,ival Data in Medical Research, Chpman & Hall, London.(1994).
2. cox D.R. and oakes. Anarysis of Survivar Data. chapmanana
Hail. London
es
of economic data (Times series _ .ror._r".rio.
simultaneous-cquation models _ .l-he simultaneous_
ancous-cquation mcthods
lApproachcs r() csrimari()n _
ntificd Uquati<tn ( l hc method of ll.S) _ listimation
of
rst squar.u (2 Sl.S))1.
s of the simple regression model _ The case of
odel - Bayesian analyis of regression modcl
with
equations Baycsian analysis of simultanuous_
-
Text Bools:
I ?*Iar
N
Gujarad. Basic llconomcrrics (3d Ed.) McGraw-Hill
Intcrnationirl. Ncw york.
Economctrics. Mc(iruw-lliit. N.* York tnrernational,,tu,lcnr,.
cdirion (19t6).
l.*?;S;"H11"*'
3'
4'
Roben S' Pindyck and Danicl L. llubinf'cld. Lconomctric
Mo4cls an4 1.conomcrric ljorcasrs.
McGrawl{ill lntcmational. Ncw york.
Koutsoyiannis. Thcory ot'tcon.mcrrics (2"d r,:d.).
McMiilan. New york (r996).
la
I
,-\
k
OP-4. Mathematical Economics:
1'
Tbe nature of mathematical economics:-fhc mathematical
versus and non-mathcmaticirl cconomics
Mathematical
Equilibrium analysis in economics: Meaning of cquilibrium
- l)arrial markcr cquilibrium - 6cncral
Equilibrium in narional incomc analysis.
Applications of liIear model: Mllkcr und nut.ional incornc
rrorJcls Luontict lnput-( )Lrrprrt mtrtJuls
Applications of dcril':tlit'c: lltc trtlttte .l'c()nrP:rrirrivc stlrrie ll'ute .l e luurgc urrtl rler.rr.ti'u - l,lr.l'rl
derivative - Application to Markr:t Modcl. National
Incomc mo<lel lntl Inplt-outprrr rnrrrlul (lcni,r.u]
function models - Dill'crsntials and dcrivarilcs l)iilcrcnrials
and poinr clusricirl, - lotal diflcr.u,tjuls Applic
anrl Nltional lncome Mtxlcl.
market equilibrium
5. Optim
maxim
6. Expon
-
inglc choice variable): (,)
of total cost function - Up*r,
ic functions: Natural expon
valucs
_
[)r.tir
c curvc.
em of growth
Applications of exponential and log functions to problems
o
6f winc sroragc problcm of timbcr cufting finding-thc rarc of growrh _
tintl
Unconstrained optimiz:tion P.oElems with several choice
variables: l)roblcm rrf'a multi-produe t firm
- Price discrimination _ Input decisions of a firm
optimization Problems with several choice variables and
equaliry constraints: ljflcct.f a eonstraint
- Finding the stationary valucs '- l.agrangian multiptier met'hod - 'forat dificrcntiul appr.ach
- An
interpretation of I-angrangian multiplfcr ] sccond
order conditions - euasi-concavity and euasiconvexily - Absolute versus rcla(ivc cxtrema
- Utiliry maximization and consumcr dcmand Homogcncous functions--- cobb-l)tluglas production
funciions - Lcast cosr combinaritrn 6f inputs Ilomochctic functions IJlasticiry.rl'sr-ibstirucion
cLS production tirncrion - cobb-l)ouglas tunction as
a special case of CES f'unct.ion.
Economic dynamics and integral calculus: l)ynamics
and intcgration
I,rom a marginll tirpcri.l r, a
total function - Invcstmcnt aird cupital frrrmlitiorr Prcscnt u-rlu. ulcash flon . l,r.usent raluu ut
perperual tlow - Doma Growth Modcl.
Application of Iirst order differerrtial equation: I)ynamics
ot'markct priuc - Solow gr.owrh rn()dcl.
'
7
-
utonomics vcrsus ccrlnomctrics
2'
3
4
8
9'
l0'
_
Text Books:
l'
2'
AIpha.C Chiang. [rundamcntal Mcthtrr]s ot' Mathcmarical I:conornics (3"r
1,,d.) Mc( iraw-llill, Ncw
York. (1984).
Taro Yamane' Mathematics of Economists: An elcmetary
survey (2"d Ed.). prentice Hall of lndia, New
Delhi. (1998)
OP- 5. Operations Research ll
l'
Kuhn-Tucker optimality conditio,s: Kuhn-'fuckcr first ordcr neccssary
optimaliry conditions - Secontl
conomic interpretation of [.agra nr:c's rn t p icrs
Lr I
mming Prohlcms
y ol
-
Sutllcicne
ualiry of convex programs
i
I
Kultn_ I uckcr
on techniques: [,inear scarch tr:chniclucs
iques - Transtbrmation mcthods tbr constraincd
solution.
mrng.
of dynamic progranrming
variablcs
gcomctrlc program
B.
-
I qeometric progams - llcducrion t() nrororl.nc
l{elatronshrp betwccl lrluur and
:[l[1-:liTi],il':::;]I1|l,:i,l,ll:r,,,r,,,.
4'
tll
glamming.
T
-Ravindran
(
-
Illusu.arir e uxunrltlus
Srochastic dynamic programming.
(icomctric proglatnuting witlr signornrals n:tlysis
3'
-
u,,,rur 2u,1, ,,,dur n,,,rspcciltl chitrtcc cttnsrlrincd linclrr progrirnrs s6dcr 1op-zcro
Philips and Solbcrg, opcrations Rcscarch: Principlcs and l)ractics .lohn
York. l9ll7).
wilcv irntl Sons Nc*
Kambo N.S' Mathcmarical propramnring I cchniqucs. L,ast-wesr press.
Ncw Delhi. ( l9g4).
(€,
3.
1
Ravindran Philips and Solberg. Operaldrrs Research: Principles and l)rlctics. J,tlrrr \\ il..i
Sons. New York. (1987).
4. Kambo N.S. Mathematical Prograrrrrnins'l'cclrniques Elst-Wesr
Dcllri (lt)lt{)
Press. Nerv
OP - 6. Statistical Quality Control
1. Statistical Process Control:
1.1 Introduction to Control Chart:
-
chart
Detection ofchanges.
1.2 Control chart principles :
charts for averages and ranges
-
Variation and the Control Chart
Behavior of variables data
-
-
Aa anribute conrrol
1.3 Control Chart for
Percent Nonconforming
-
control charts.
Charts for number
Standard Deviation chart - Average (.r
chart - Evaluation ofcontrol charls.
-
-
Control
Charrs for
attributes
of Nonconformities - OC curves fbr
1.4 Control Charts forvariables: Individuals (.r) chan - Rational suburoups
-
-
Normal distribution
General principles ofcontrol charts.
attributes: Charts for number of Pieces Nonconforming
-
bar) chart
-
Median (x
-
-
bar) chart
Range (R)chart
-
Midrange (;!/)
1.5 Special Control Charts: Cumulative Sum Control Charts - The exponentiallv rveighted
moving average control charts - Modified or Reject control limits for x-bar charts - Acceptance
control charts.
Methods tor'Quality lmprovenrcrrt: Graphical Methods fbr euality
Proccss ('ontrol
Techniques - Specification t.imits. Toleranccs lnd related tcclrniqucs.
2.
3.
AcceptanceSampling:
3.1 Single and double attribute sampling: Sarnpling risks
sampling plans
-
-
-
Sampling variations
-
Types of
Double sampling plans.
3.2 Sequential and Muttiple attribute sampling plans: Item by item sequential sampling plans
- Group sequential plans - Derivation of Matched Plans.
3.3 Attribute Sampling Tables: ANSI / ASQC zl.4 - 198t. - The Dodge-Romig System - LeL
index system.
Single sampling
3.4 Special Attribute sampling procedures: Continuous sampling plans
plans
Text Book
1.
-
Chain Sampling plan.
-
Skip-Lot sampling
Modern methods for quality control and improvement. Wadsworth, Stephens and Godliey. John
Wiley and Sons ( t 986).
Reference Books:
l. Statistical Quality Control. E.L. Crant and R.S. Leaven Worth. McGraw Hill, New York. (1996).
OP
- 7. Industrial Statistics
l.
2.
3.
4.
Quality and its measure: Quality and reliability
sigma methodology.
-
The Taguchi Methodology
-
The six
Data and distributions: Non-parametric methods - Probability plotting
- Point and inrerval
Statistical Process conrrol.
Reliubility flnd Rates of Failure: Reliability Characterizations - Consrant l'ailure rate rnodel
- Time dependent fuilure rates - Component failures and failure models - Replacements,
estimates
-
Loads, Capacity and Reliability: Reliability with single loading
factors
-
Repetitive loading
-
-
Reliability and safety
Single failure modes & Combined failure modes.
5. Reliability testing; Reliability enhancement procedures - Non-parametric methods Censored testing - Accelerated life testing - constant failure rate estimates.
6. Redundancy: Active and stand by redundancy - redundancy limitations
- Multiple
redundant systems - Redundancy allocation - Redundancy in complex configuration.
7 Maintained systems: Preventive maintenance
- Conective maintenance - Repair: revealed
failures - Testing and repair: unrevealed failures.
8. Failure interactions: Markov anrlvsis reliabilitl'rvith stand bv svstcrns nrulticomponent system - availability.
9. System safety analysis: Product and equipment hazards - Human error - Methods of
analysis - Fault tree construction - Direction evaluation of fault trees - Fault tree evaiuation
by cut sets.
Text Books:
1.
Introduction to reliability engineering: E.E. Lewis, John Wiley and Sons. New York.2n'r Ed.
1
996.
t
!'
/^
gt -j
\-L2/
|
.Acluariat Marhcrnarics _
uasrc r\lathcntatics rrf t,.;,,.,...._.of
r.
.l.
r;cn.'rat
;
3
iLli;":"t"'.1"'rics
'J'trc
l"illarrce: \irrrPlu tttLe.cst (
.,rp.untJ inreresr sinrprc
- "r'rrt/rL annuiri
dlrnutlles
utues - ()rdinary,
a,in;;;;;"tt
Ecoltorrri..,rf
r.....oI trtstr.attcc:
,ffi:|;"-rl,T[rnodet.for
4 s,-;,,iti,,il",l.[I"
lrtrli]-r'
rlre.r'r
a short rime:
rrrsur...ec arrtl
utirity
crcr,c,r.s ,r.in.s urancc
,d ultirrrate
trrbrcs.
stams
_
h
A.s.sr
' r')i(
ti.nltl
period:
.1.h,
laims
ron.s
8 ffi,ili1,;kl1iil:l;Jil.,',:[ifJl,l.iii i.l.i],+il:1ilX,;:i,i[;lt:l*n,
Tex
iiifiit#flilimatingir,"
- Sulcction of hasic
k) thc distribution of
c,,erricien, _,,iscrc,c
inal,i,r,ur m.ttcr- srop-ross
- ('otnpound st:lttrsesi ('()ntlngunt
prohuhilitic.s
conr|]:il]'';ll}"1'T Ner rcrrtirrrri,,,nt','.u.,'r.r.
ts
nt
te' l.exis di:rgrunr --
Population
larvs
abilitics and cxpcctations
tl()n-unifi)rm distributi<ln.t.-
1)rliss<ln
t,
f,. .f"..r;,rir,;.
S.nre anur-ytical
.l.he
- Spe
lrv:rlulrriori-s
ttcs of ctlmpound
f
lgcs
luarion
10.
()ptimal
ixl':r"1ii,ilxr;ililir;lt [lT*:rfffr,.:,Tlr.']::;,:]il:,.:,
- I'ile ttrhles
the'r lil'r: t:rlrlc lirncriprr.s -.
e.
-
rvrodcts
,\
-
t)ynuri.r.
stationary and srabrc popurari,n.s
chr;ck. 3,d l:<J. tVtg(jexw
icrhcr
rragrrer
and
llill
Kogakusha
l.td. .lirkyo.
ll.ll. llickma.n.l.(....krnc.s l).A
r.l. J. r. ,. 1. i-.r.',r."ilr,'.i1r,.anrl Ncshitr (,.J.
,i:*
_ lnsurancg payablc
ar thc
uncl of thc ycar
sun,ival _ Continuous
litc annuitics
.
_ Discrstc lif.c
ri,",irfrr,iix annuitius with
ln cquations - comprctc
,nnri,i"r-ir.cdiarc and
L'onrnruturion flnction
alucs _ Insurancc options _
As.sct sharcs _ l:xpcricncu
ot'annuity hc_nctits._ family
inc<lmc in.surancc _
t:tcxitrtc pt:rn
Prrxftrt.la fiUfriii,), hcnctirs lirr
l'
inal tirndinu _ Accrual
ot.Acruarial liahiliry _ Ilasic
iut crsr ,.ir,.1.1 _
ngg*g*""liri'n,.,r,.,.rs _ rlasic
f activc and rctircd ,"rU"-.r.Actuarial Mathematics'
Ilowers
rJr):9::.b.. H.u, Hickman
Socicry or Acruarics.
i"*".'iiir,"l,:
*''
-
i;;, ((,h,;;;,;.^;:.
D.A
and Nesbitt
]on9s
;:, {,!.,
r0. r4. | 5. r6. rnrr re).
c.J.
.
\
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a
-
./
a
In'r\IqR-fT\.
(
o!r cAI -^lrT
",I-.stract)
M.sc. ,statistics - addltion in the syl1aL'us of rv,gernester changes ln thc-: Jst Semeater - apcroved - orders issued.
Grir-tR- T, arrn 'ratDrlr Ia I / J 5.:TIo.-
c r/Jt/.o5c/ee
(-t)
Callcut Itniversity P.O. , dt-ted 9.9.02.
Read: 1) U.o. cAr,/J7/4756/99, dared 31,/lO/21)1.
2) l4i nrrtes of meetin-r of :!oard of .studies in .statistics
(pcl held on 2a/7/20t2 ancl 't/5/2oo2.
3) Irlnu.tes of meeting of Acaden,ic council held on
7
/6/2coz
glf:?
The Scheme :nd Syllabus of N.Sc Statlsrlcs (sr pattern) were
lmpremente-'d i ith ef ;',-'.--t Erom 2c01 aclmission onwrrds vide rr.o. cl.ted
as fst Paper
(2) The meetinq of Board of -studies jn statlstlcs (p c) held on
28/1/2Oo2, resolved to inchr:-]-- two a.lriitirnal modufes V and Vf
in the TV th semester.
Y!!_Elgl", E-i o.s!:tiqqcs i
4 . 1
4 . !
d . E
4. 4
.;urvlval ..tnalysis (o p-2)
.Statlsti ca I genetics and Clinlca I tria Is (O p-l
statistidal Ecafocry and Demoqranhy (o p-ff)
Dractic.rl fff based on 4.1, 4.2 and 4.3.
2)
Yf _th_Modu_le:
4 . 1
4. 2
4. 3
4.4
Survlval Analysis (o p-Z)
Statistlcal Decision tte6ry'End".eayeslan analy6$s
(o !r-10 )
Applied Stoaehastic Model and Time series
Lnalysls (o p-l1)
irractic-I _ rrr based on 4.1 to ll .3.
(3) Th,- Board 6f stud jes .1s-: rnodif ied .the syll.rhus of r sai ester
I\/.Sc StatistiCS. (ie) n,r.or I and F.f D€E Tf - lro chanqeS.
Paper r ff - No chances. P.r per fV - llodule Iff : rrram Cfrar$ier
type A Series, Edoeworth form of type A..series are deleted.
Contd...P/2.
'i\
rrodul-e Tv : l.ul-tiple and psrtical C-oreelation defjnJtion
and applications only.
ro derivations of, partta]- qn.:]
Multiple correlation Coefficient. paper V - Modul,e V craphics solution of Lpp 16 deLeted.
4)
s)
l.
The Board of .Studies lt its another meeting held on 1/,.LOVZ
r,icommended to use scientific non trrogr.jrrfitable ca].cUl6ggsg
for examinauions :'n theory pFpers aLso.
The Boar:d of Studles afso reconrrerxled that as the praeticelg
1n lr.Sc Statistics involve. data AnaJ-ysis, Computer proqramminc, etc., the practical pap r may be treated similar to
that of theory Dapers ruhilrr calcrrLatjno teachingJ wrrk load.
6)
The meetj.nq of Acadernic Councif held on 1/o/2CC2, approved
the mj.nutes of meetings of Board of Studies held on 28/l/?-OO2
and 'l ,/>/2oc'2 "
.t)
Sanction has been acc,rrded for the jmr,lementatJon of decisj-on
of Bo.rrd of Sludies
mentioned in papa 2,3,4 and 5 with
'r002
effect f rom
admission onhf.rds.
8)
Orders are issued accordinqly..
sd/- ngprr.j\. ?EGTSTRAR
(C r, e r)
rbr o.Er:rsTRlq.
To
1)
2)
ggPl--le-i
PrinclpaLs of CoIleqes offerin€l
M.Sc ,Statlstlcs.
of the Dspartment of i'iati"tics,
Ihiversity of Ca ]l cut.
Hearr
.
Controller of Dcamlnatlon.
Irniversj ty fnformation Centres.
Ihlvarsjty Llxraryr/
SF,/
FC
'
r
FoRi,7\
1DqD,/ BV ORnrrR:
qEC.nTn\r oFI.TC."R.
, vkv/t9/e
E
-/
I''r: F.S IT'Y OF C/ILICUI,
U]\,
(.;\bstraet
l,l .
sc statisi;ics
ier )
(s.:ni.-,s
approvecl - orc'ers -issuel
)
_. change
s in the pr:rcti._ .
============,__===
r-iEl"LRAL AND ACAI:EI .f C i
cAi/J1/606€,/sg
===
l;ated, Calicut
'J ,
S EC,j
,-.rpeES
r,
Uni.v_tr:3i-ty F.r . , I1.7.2003
========
Read:-1)tii-nutcs
he.ld on
2
3
)Minur_cs
)l4inutes
Boari of Stuclies in;,:atisti-cs (pC)
F'aeulty of Science held ttrr
. 10.3.200.-?.
ecademic council held
"i- 21.3.2nc3.
qE!EB
:
The meetino of Boarc.: of .S1sdi..s
in Statislics
on 20'2'2003, recomniencred i:o'revJ.se
the Fraci:ical
l'.Sc Statistics as foI .O,,7s:
(fC1 hr:1i
paper._e
of
) f,..Llarclirrc the. paF€:r 3.5 Iract,ieal f T. of Semestir
3 anc_l
Fractical 4 -4 cf Ssrae ste r 4, the soercl
macre a cetaired
discussj.on ur.,d resolvei Lire followino.
since 'enough nui,.ber: of eomputers ar€,
not avairab.r i i,r
son,e centre s for eoncucLi-nE
the lractical .rx<lrl.ia.]t_i ons,
students are afloilei tc use sclentific
calcul_at.ors for i,ire
practical exarnination. 1,h= eXaminati-on
be concluctcu as
trracticar r of 2ncr- s:iiis-,ctLr (Fppe r 2.5 practical
r ) -r,op,iqg
for the practical- .--xamir at_-ion. fgr,
Faper 1.5 Fractical If ai e base.d on
laper 3.1
:
l:uftivariafe Analysis
Faper 3.2
i
i1na.l--,sis t/ sampl= survey Lepigns
Fraper 3 .3
:
Lesign an<) apalysis of Exper.ments
Fap,..r 3.4
;
F r:oc raiiuL,_in9 in C l.* ancl
S ta tis t j ca I
a
Computinq
the internal c;-arriir.ation for the
Fapers 3.5 ano
usilc eomFuters
L,) Regarcr-i-nq t-lte trrc ject (Fapcr
4.5 ) in .the 4th. semcstcr it i-q
rcsol-rrec-r that the Frojeet iiiay
be of research (theor;tical)
or of practical naturi-: to.tn uf inclivicluallr;,
Eacir stu,:,.i-t
has to subrnit a reFort on tr-rc work <lone
by
himl-rer
at t'e
.
of 4th, semegtert
.encl
IJow,,rver
4
_
.4 are to
ice concluctocl
_
(
con tcl . .
.2)
\
t
- 2.-
I ) Ttre meeting or' Faeuli" of scienc€ hol-cl ,:n 10.3.
approved the minutEs or': .rc-,ard of SEuilie s.
2OC3,
3) The meetinc of -rcaCreric Council heIJ on 2'l .3.2003,
approvecl .the m.inutes of Bcard of Stuct i,-.s as apL,rovei by ihi'I'aculty of .Scic-ncc a,.cl al-so the ninut. s of FacuI!y of Scir'-rrC€.
) ,rsapction has b,.'.n accorclecr for imp1er,,:;rtlng the
clecision of Eioarc-r of' .ltul'i-- s.
4
5
) orders are issuer:
se/R+GISl't,Ak 1I ( :.' .-..1
I OT RI-GISI'I1AR
Asrc,t'.
'I'o
1)T'he Frincipal- o1 tli: CoIlege of feting
t{.Sc Statistics
2)H/T, o'Statistics
Copy to:- Ctr/ar</DR(i:.Sc ),/
-
t
.
University 1ir:icE,r,QLion Centresr/
Unlv=rsity Licr:arY
s\ /lc
ORD,'R
SECTIOI] T]I'FTCER
ek/l,5.'t/
)
Fly UP