Time Allowed: 3 Hours Maximum Marks: 300
Caniliilates shouldaJtempt Questions 1 and 5 which arecompulsory, andanythreeojtheremaining
questions selecting oJ least one questionjrom e(f£h Section.
Assume suitahle data ifconsiderednecessary andindicntethe sameclearly.

SEcnONA
Attempt any five sub-parts of the following
(a)Distinguish between Process Control and Product Control How do we achieve them?

(b)Obtain the OC function of x bar control chart. Explain its use.

(c)Define failure rate function and obtain for the Weibull time-to-failure distribution

(d)Define irreducible Markov chain Show that in an irreducible Markov chain, all states are of the same type

What is an queue? Show that the expected number of busy servers In an queue in steady state is Crow=lamda/mew and that the expected number of idle servers is

(f)Explain the Simplex Algorithm for solving a linear programming problem.

Explain the construction and use of c-chart.

(b)Define system failure rate. Show that In a series system conSisting of n Independent components, failure rate is equal to the sum of the failure rates of its components, and it is not true for parallel system.

(c)Obtain the maximum likelihood estimate of the mean for the exponential model based on a censored sample.

Solve the following LP problem graphically
Maxmise Z 3Xl +2x2 subject to <img src='./qimages/1118-3a.jpg'>
(b)Explain the assignment problem Show that an aSSignment problem can be solved by the transportation technique

(c)Define renewal density and renewal function. Show that the renewal function for an ordinaty renewal process is given by
<img src='./qimages/1118-3c.jpg'>
4.(a)Explain the construction and use of sampling plans for stipulated producer's and consumer's risks. Flow do we choose the best sampling plan?

(b)What is redundancy? Is redundancy at the component level more effective than redundancy at the system level? Justify your answer

What lS an inventoty system 1 ClasSify and discuss the different types of costs involved in an inventory system.

let x1,x1......xn be a random sample from an N(mew,sigma2) distribution sigma2 known). Let <img src='./qimages/1118-4d.jpg'> be a statistic. Explain how the well-known statistical software packages like SPSS can be used to find thed distribution of T
SElmON B
Attempt any five sub-parts of the followmg
(a)Describe the method 0f link relatives for isolating seasonal variations in a time series.

(b)What are the different tests a good index number should satisfy? How many of them are satisfied by the Fisher's ideal index number?

(c)What are the principal publications which provide data on agriculture, industrial production, trade and prices?
(d)Explain and interpret the following


Vital rates and ratios
Fertility rate
Morbidity rate
How are population projections made?

Explain the use of factor analysis in psychometry.

What is stationary time series What are the different schemes or models which may account for oscillatory movements in a stationary time series?

Discuss briefly the various steps for constructing a whole sale price index number.

Explain briefly the problem of multicollinearity in general linear models, its consequences and solutions.

Derive Makeham's law stating clearly the underlying assumptions. Also explain how the constants in the Makeham's law can be ascertained from four equidistant values of 1x.
What are the uses of stable and quaSi-stable population techniques in estimation of demographic parameters?
Define general fertility rate and age specific fertility rate (ASFR) Describe the methods for calculating these fertility rates. Also indicate why ASFR is considered as an improvement over GER.
What are the methods of collection of official statistics on industrial production and trade? What are their limitations and reliability?
Explain the functions of NSSO as a part of the present statistical system in India
Explain the different methods of combining and comparing scores in several tests, stating clearly the assumptions made in each case.
What are intelligence tests and how are they used in measuring intelligence?