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I II!S.!CHIO I ot li

l STATISTICS

PAPER· I SECTION A

I

I. An<wcr nnyfour:

2.

(a) Clloose Uut.corr~tutll!Wct

(b)

tl) Probabilily of gotting at IC<Js! one G in rolling lhreo dice iS ---l ~-~-~-lH] (ii) J'robnbilily of a rnndoonJy s.:l.cled leap yeat• c:on~Lining 53 Sundays ill __ _

[~. s~ · :~] (iii) has \he some meon nnd vnrinnce, [Normal. BinomioL Poi.,on

distribtttion I (iv ) i\ludion lc~i ill nttpliud 10 leNL whctltct LWO

tendo-ncie!;. [eorrelated. independcnL paire<l) ____ groups differ tn central

Mau;h X wi~J Y:

X y

( t j Axiomatic aprmlnc.h (A) Median 11!01

(2) l..e:ast .square.~ method (B ) Probability theory

(3) Nou·p;ttantclxic mt>~tod !CI Estimate.

l•l) Consistent (D) Nom1al equations

(~) Supply the missiug wot-d(s):

(i) rn~ lin t moment about mean i.s ____ _ (ii) Mnthc:matie"l expectation i• llte . um of prodUL~ of \ 'al'iale l'lllucs with corre• JXmdin.,.g __ _

(iii) le.<tos applied tO tc;;t g<><ldnCl!ii ol'tit.

(iv ) Mo.ximum llkelihood ~timolors ~re if suJl'icient co;t imJlOl'S exiRl

(d) (i) Stale two importllnl Jl i'Ojler1 i~ of maxirttmn likelihood estimntors.

( ii) Give ~"' formula of r} for testing goOdtt<!!<S t>ffiL

(iii) Ci ive two exnmples nf PoL~son distribution,

(iv) St•le tlla •ddition lhoorom or pt'obability.

(e) (i) G·ive ~te value.< of Ute mean and l.be S'iandatd d;:viatioo of ~ standard normal dis tribution.

(•)

(ii ) C'~n yqu h:tVe a neg~th•e value l)f prob•bility? Justify yl)ur nn~"er,

(iii) ln I<!!< ling ~oodncss <Ill' it computed value or ')(, is great01· than lhe oorrcspondlng lllble V;Jhoe. Jntuo:pt\:.1 lite rcsulL

(iv) What nn: no1111nl equttllon' in the method ol' le:~t ~<rua,es?

Give Ute diJfc-r10111 definition~ or prl>bability. Mcntioull1e lintilntions :md udvontngcs uf cncb.

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1 ''"" (b) 'Mutually .:>Kdush•.: ~Will' w1d iodepond<ltl ~vents <Ire not ~qtthaleut iil~a.··· El:lburo1a witl• ",\":!ntpl<:s.

(•) Probability ora boy passing a p:u1i"ular examiuation i~ ~aud that ul' a girlts ~ Wbut I;; the

prub.tbility that al.l~n::t une ofll't~m p llS!'CS tJt• ~xarninnllon?

(d) l\tnlo azty.,'~ 11\c~rum nttd cxpl:tin it~ Mignilicwt~~-

( " )

(b)

DitlCr.:nLi111~ betw~en paran~tricnnd mm4parnmelri~ nprnoachl.'$ h) lh~ sttnistk"UI inf"r~nc.e.

\\'rite~ note on '"''IU'al limit the() rem,

(~) \\~IOlt~ ~h•ract.,-istic fun<1.iOn'l Slate its imponnn~e.

(d) Show by :m example lhm an e!llintnte may ba unbii~sed buJ 1101 consislttlL

( :0) D<line unbiasedoass of:m estimnll)l'. Ob1aio unbiased estimate ur r:r front N 11~ a:) if I' is Jc;nnwn

fhl Nam~ some siwmiuns wh<<' PoisSon dislribution i• "''P<C!<d. Whm ar< tha impot1an1 "hur:o~teristics of " Poi."on distrihuunn? Is the Malon•~•tl, "the nt<an and lh< smndard deviotitm or a PniAAOn distribution nrC" 5 nnd J r~<\pci:lively' ~ corroct?

\I!) • An ~'Siimator IS" suJ1id"ul •IUii~lic if tho! pmbnbility d<OSII)" function Call b~ facturiscd uno two purts- onc <kpond~ol o1tly on th~ stntistlc uod the pammetcr ruul the oth\!l' mdcpcudcnt of the p:tnUucler'. Discuss.

(d) Write stal~mcm of Cmmer·Rao mectunlhy ood IITite regulru:il)· conditiotlS of Cr.amer-Ruo inequality.

SEC'riON B

5. Answ~r an~ four:

(n) Fillttp the blanks:

(i) ln sunple randotu sampling wi1h replacem•m tlt• twlmlb"r or possible s:unples of ~iz• 3 l'mru:. p<lpulation of.•iu 10 is _____ _

(ii) V,..,.., "'''~'~"""" nnd V~""~"ma..t oc,'llrin 1he order ____ _

(iii) 1l1e smodnrd ~rror of meM in simple random samplmg \\ithoul replaocm.!m 1S giv.:n hy __ _

(ivl ·nto limik, of partial correlation rootlkienlu~-----

(b) Compl_.e tlte P.,'{OV A wbl~;

Sm.JraJ rLf. llcpftcmtion Main Plot

,_1 'l'rMtn1eu1 '1'· 1 J,'rror (o) -S<Jl>-plot 'CI'e&lment r-J Int. (M.P'r "'SPT) -Errodbl -Totnl -

(o) Two rcgrrssinn lin"s ate

2~· Jx = Jii

s.s. M.S. s.• -

- S/ E• -• s• -s> -II - -5' -

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Ss • S} = 75

Fina thel'oint (l'. i') .

(d ) M:ttch X withY:

\ II (2)

(.>)

(ol)

Ermr (h)

Control blv~k

J>roportiono l 3lJO<:lltJou

Cumubtivc tolnl method

y

(A) Slrnlllicd ~amp lin~;

.(B) Split-plot d.::slgn

(C) PPS S:Uilt>ling

(0) Confuunding

(.:) Clioose lfte eorr..ct one:

(ii)

I iii)

(ivl

l.n o ne unit is selected "I rnndoru. and the othe-r unillli :ara automaticaHv determined ls1mple random s:unpling, PPS ~ampling. system;~tic sam pi in g) ·

1 n - number nf o"Cptico6nus for e3ch n-e•tmout should be: some. ICRD. LSD. RBDl

'Ote __ interaction is genemlly conlounded. flnghc:<t ordor. lowest order, 1n.1in ~n·cctsl

--,---=-- of a p.1rtiol cllfT(;lation oveftict.cnt '" gh en by the number of variable>~ 11 hose etTocl• are ignored. I Rate. Order. Po" erl

(i. (o) Show that the JlrObabili!) of selection of • .speoilied unit ot the rlrst dnow or ony ~ubscctuont draw m ~omple random samrling rem.• ins tbe same.

7.

j b) ·systemoGc ~amplong may be consodered as a particu lor oase <rl' chljter. .. mpling '. Discns~.

(c:) Why n:gru.>itm "']Uailon. oru called prc:dO,tion «JU.t6ml> 1 Now do"" the <l<:<."'llr.1>!Y of pncdic!loo d'<l'end on correction coafficicnl'l

(d) What is lh~ null JJ)'llDihesis of medinn test'/ How iL is apJllled In pt>ctlce'l

(n)

(II j

\\'h•t i~ multiple regreo<sinn7 rvtenlilulthc nssumption~ >nd prrtpcrtiet~ of multiple regrcs~ion.

Shllw that th" Jlroducl of the l\111 rt:grt\!sion CQ<::rJic,ionL' is equal to the square uJ' U1e co•rolati.,n cuc1liei<.11t.

(c) lln<ler what <ltuatioM split-plot desl~ 3 •JlJll'Optiatc? l:kscribe the layout procedure of snlit­pl<•t design.

(d) Folio\\ ing 19 tho layout of a replication of to 2' f~~iori•I I:'CJl•-rimr:nt confounding, ••1me effect:

Block 1 Dlok.Jl

a!)cd • ad bed (TJ obc

ot c

ob olld

od .l~

~c d

bd b

Detw tthe confounded e:J'fa:t

8, (:o) SIJ>te.lh.: merils and d.:ut•o•its ol' cutnpl.,tely rnndotW>ed design and tandutuiJ\c:d block do:.sigrc

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4 of6 (b) \Vltat is l.Dtin squore de•ign ? Wby tl1iS design is not Vet') COihll10nly ndoptc:d in fie.ld

experiments '/ Mention the rt~~triction(•) of the design. i( any.

(c) Sirople.:orrclation coefficients >tc given a.< follows:

r1z= 0.53. r1, = 11.45. ru = 0.80

Computer fJ:!J llOd Rt.:n·

I d) Wha t is ~n~lysis of variance·! Describe the assumptions of analysis of variance.

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~~=== STATISTICS

PAPER·It SECTION A

(JJHiustrial SlatistiCJ< und Optimis.Cion Tccbniqu.s)

I. Aliempt any four:

(a) Wlml i£ J s l• lisliClll process conu•oYI

{b) Wl••• nre tl1o concepts of relinbility?

(e) Exploin scn~.itivity ~nnlysi>.

(d ) Explnin diffcrentl)'Jl'=• of costs involved in inVentory control.

(co) Wlml is transition pmbablllty llllltrix?

2. I~) Wbnl nre the cnu~e. of vati•tioo in Sllllistic;~l Qtlll.lity Control?

(b) EXJ>I:oin control charts ror :111ribuh:s.

(c) Explain s inglu ampling plan and determine it~ parameters.

3. (a) Explain tl1c role of Wcibull distribution in reliability theory,

(b) Explain cemored nnd truncuted experim~nl' for exponential onQdels.

(c) l~xpiAin uptim isMion thc:<lf)' l!iving s uitable example.

4. (a) F.."JJIrtin !he two-person zero--surngamd by givine an illustrnlion.

(b) Obtrun the .Economic Order Quantity in case of deterministic model

cc) Explain M/1\(~.l and GIM! l in queues.

J

(I()!

( 10)

( I())

( 101

(10)

<13J

(131

I 14)

( 13)

( 13)

(13)

!141

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6 uro

SECTIONB (QuiDiitJ.Un> &on om ics and Offici :a! 5tlatlstia<)

s. Attempt any tour: C•) Eli:Jll•in dilll:rentoompont:nlll ofTimc Seril:l<.

('Ill)

(b) Wh}' is Fisher's formulo for Index nwnbc:lll considered us >II ' idetll" one1

( lH)

(c) E:.pluio ![<1lcraUsed leustsquure method of eKtimation.

{10)

(d) E:~:plain the noed for demogropltiednta.

t 1\))

( 10)

&_ (n) Wbnli> • problem oflndol( Nwnbo!r& 7 E:'!ploin th• ohuic.: uf • bose your of lndc_x NIUilllcrs.

( 13)

(b) Whnlis 'nnu:; Revcr.o l Te>t oflnd.:.x Numb«s?

( 13)

(e) Write sh01t noll.-s on (i) Co. t of Living Jnd<!l<: Number 011d (ii)Indu.o;tri:ol PrOduction.

(14)

7. (n) Wlutis multic.otllitcoarity ? Espi:Jin giving 011 illustration.

( 13)

(b) \\·rite about lwo-slllg.: lonst •qu.nrus n1cthod of .. lituntion.

( 14)

(c) Dc$cnne vMiOu.s method" of collection of offidnl•lntjstics in India.

8. (•) DoHu~ ( i) Crude DCJ~Ih Rotc. (ii) Infant Morllllit) Rnld, 11t1d ( iii) Sll!ltdtlrdiJ;cd DeAib Rl!te.

(13)

(b) Doscribc usos o[lif,. t.blcs.

( 13)

(c) WIIJit is psyoliOlllctry? llow is C1ator rumly&is useful in l'•ychomttry7

c 14)