Time Allowed: 3 Hours Maximum Marks: 300
SEcnONA
Attempt any five sub-parts of the following
With reference to control charts, distinguish between warning limits and action limits, and
Type I and Type II errors

Explain the construction and use ofX and R charts

Explain the concepts 0f 'availability' and 'maintainability'

Describe the different models used In Operations Research and state the general methods for solvmin them

What iS queuing process? Obtain the probability generating function for the queue length of M 1Mil queueing model and obtain the mean queue Size

ConSlder the Markov chain with the states and with tranSlhon probability matrix

3/4 1/4 0
1/4 1/2 1/4
0 3/4 1/3
and the intial distribution
P(Xo 1,2
Obtain the value of
P(Xo X1 Xo

Explain the statistical baS! s and construction of p and np charts

Explain With examples series and parallel systems A series system of n components is such that each component has a failure distribution giVen by

1_e-(x/alpha)alpha;x>-0.
Find the failure distribution of the system assuming that the components operate Independently and n is large. What will be !hi s distribution under paralle1 connection?
Explain the measuring 0f censored and truncated samples. When are these used?

solve by Big-M method the following LP problem
Maximize
subJect to
x1+3x2<-3
x2<-4c

(b)What are replacement problems? Discuss such a problem is which items detenorate With time and the value of money remams the same as per passage of time

What do you understand by 'recurrent' and 'tranSient' states of a discrete parameter Markov chain?
<img src='./qimages/1097-3c.jpg'>
Show that a state J is recurrent If and on! y If

1fa stateJ is tranSient, then Pijn-0 for all i.
What do you understand by sampling inspection plan for van abIes? Explain how it

differences from the sampling inspection plan for attributes State the use of Dodge-Roming tables

What 1s redundancy? Explain the use of redundancy is reliability Improvement

Describe a POisson process Obtain the distribution 0f lnterarrival times is a POisson pro cess

What are SPSS packages? Explain their uses


SeCTION B
Attempt any five sub-parts of the following
Describe the method of moving averages for determing the trend component of a time series. How is trend eliminated?

Define Fisher's Ideal index number Why is it called 1deal?

What are the principal publications which proVide data on ,industrial production, foreign exchange and mining activity?
Define and interpret the following measures
(i)Infant mortality rate
(ii)Expectation of life
(iii)Density of population
Define a 10gistic curve and examine its suitability as a growth model
WhatiS the 'validity' 0f a test? How lS it measured?
What are the different methods for determining the cyclical component of a time Describe 'periodogram analyses'
Describe the essential steps for the construction 0f an index number of industrial production "
(c)Obtain the generalized least squares technique for estimating the coeffiCients of a linear model Comp are this With ordinary least squares estimation
Define crude and standardized death rates. calculating standardized death rates Describe the direct and indirect methods for
Explain the various columns of a life table giving the relationship between them abridged life table?
Write a note on health surveys and ho spital statistics
What are the various offiCial agenCies responsible for data collection? Discuss their roles
Describe the present official statistical system in India dealing with collection of agricultural statistics
Why is it conSidered deSlfable to convert given raw scores is to some standard scores? Define 'standardized scores' and 'normalized scores', and describe how these are denved
Describe any two methods commonly used for computing the 'reliability' test WhatlS the effect of length ening of a test on its reliability?