Time Allowed: 3 Hours Maximum Marks: 300
Instructions COJU!ilIJltes sIwuId aJte""tqueslions 1 and5 whkh are compulsory, and Il1!V three ofthe remaining
questionssekctingaJkastonefrom eachSection.
suitoIJIe t!JIb ifconsitIeretlnecesswy andintIkaJe the snme ckarly.


SECTION A
Attempt any flue sub-parts

Explain the concept of rational sub groupmg for control chart purpose Descnbe two schemes based on order 0f pro ducti on m this context


Denve an unknown Sigma vanable sampling plan when there lS only an upper speclfication limit on the quality charactenstic m acceptance sampling


Describe Type Type II and random censonng of samples


Fonnulate a general linear progranumng problem Define slack and surplus vanables and explam thelr role m this context


Outline two different types 0f replacement model s


Describe a queuemg system Stale the measures of perfonnance of the Single server exponential queue


Explam the statistical baSiS of a p-chart Describ e ltS construction when the sub group Size n lS

fixed and varymg


Describe the double sampling attributes plan for lot disposition. Denve ltS OC and ASN functions. WhatlS curtailed mspection?


PrO) ectWetbulldistribution asafailure model Denveitshazardfuncti on WhatlSabalb -tub curve?


Obtam a necessary and suffiaent condition for a baslC feasible solution of a LPP to be an optimal solution


Denve the formula for EOQ when


demand is delerlll1n1stic and continuous


shortages are allowed, and
production is detenmrustic and continuous
State the assumptions made





The purchase cost of an eqUipment is C and denotes the mamtenance cost

function, where x is the age of the eqUlpment Assummg the salvage value to be zero, obtam an optimal replacement policy Also delermme the optimal replacement time when C 50 and 0


WhatlS a CUSUM control chart? How are the parameters of the V-mask for such a chart delenmned?


Explam the concepts of AOQ and ATI for rectifying mspection by attributes What is AOQL?


Define a Markov cham How are the states of a Markov cham clasSified? In a finite Markov cham, can all the states be tranSient? Justify


Write bnefly on the software package SPSS



SEcnON B
Attempt any five sub-parts

Define a time senes and its mam components. Explam the tents stationarity and mvertibility m time senes


Describe a general linear model m K mdependent van abIes Justify the lncluSion of a random error term m this model


Explam Durbin-Watson test for auto correlation maGLM


Define net reproduction rate. How is this rate constructed and mterpreted?


Examme the use 0f stable popul ali on conceptm estimation of demo graphic parameters


What 1s test rellabili ty? Describ e a metho d 0f measunng reliability 0f a test


Bnefly discuss the followmg m time sen es analySl s


Detemunation of trend


Forecasting




Explam 1dentification problem m a Simultaneous equation model. State, without proo£ the

rank and order conditions of 1denti fiability Also outline the two-stage least squares metho d of estimation


Spec1fy the time and factor reversal tests for a pnce mdex number Illustrate by a standard pnce mdex number which satisfies both these tests, provmg your clatm


PrO) ect the 10 g1stic curve as a mo del of human population growth and di scuss its limitati ons


"
Explam the baSic assumptions while constructing a hfe table In usual notations, prove



What are the uses 0f a life table?
Compute the crude and standardized death rates for Population g1ven the followmg
mfonnation
".". group I St<>"dard (ym15) populalion
_10 . 20 I


10
20 .60 flbov,r60
""
Interpret the results
Nod



5
«

20 ,,"puhnon
"
""

'500
«00

""

No. of


6


"


Outline an applicati on 0f factor anal ym


Write bnefly on


metods 0f collection of 0ffia al statisti cs m Indi a


thetrreliability and limitations




WhatlS mtelligence quotient and how lS 1t constructed?


Write a bnef note on Central Statistical Organ1zation