l. A new.paper boy has the following probabilities or telling a magazine

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Coat of a copy is 30 paise and sale price is 50 paise. He cannot return unsold copies. How many copies should he order? Solve by EOL criterion.

Find an optimum solution to the following transportation problem
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A supermarket has two sales girls at the sales counters. If the service time for each customer is exponential with a mean of 4 minutes, and if the people arrive in a Poisson fashion at the rate of 10 an hour, then calculate the probability that a customer has to wait for being served and the expected percentage of idle time for each salesgirl if a customer has to wait, what is the expected length of his waiting time?


Let h be the reliability function of a coherent system. Then prove that
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Obtain the reliability function and the hazard function for the Weibull distribution.

2.
An electronic device constants or four components, each of which must function for the system to Function. The system reliability can be improved by installing parallel units in one or more of the components. The reliability (RJ of a component with one, two or three parallel units and the corresponding cost are as given below. The maximum amount available for this device is 100.
The problem is to determine the number of parallel units in each component. Use dynamic programming to solve the problem
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The following network diagram represents activities associated with a project

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Determine the (i)critical path, total and free floats and (iii)duration of the project that will have 95 percent chance of being completed.

25 items were placed on test and the test was terminated after a pre-assigned

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distribution is weibull with shape parameter equal to then compute m.l.e. of the scale parameter and estimated standard error of it.



Develop an exact test statistic for testing the shape parameter of the gamma distribution p when the scale parameter a is known, based on moment estimator of the shape parameter and against right-sided alternative.

For a prototype test vehicle, electrical failures for the engine operation occurred at the following kilometers 28820, 36707, 46128 and 68345. The total test schedule was 72000 kilometers. Estimate the reliability function assuming exponential electrical failures. Also estimate the
kilometere at which 10% of the vehicles will have failed.


3. Discuss on hospital records and ad hoc surveys in relation to vital statistics information.

Discuss internal migrations. rural-urban migrations and international migrations.

Define crude and specific death rates. Explain clearly the purpose of standardizing death rates.


Given that the complete expectations or life at ages 25 and 26 for a specific group are 22·08 and 21·93 years, respectively, The number of people living at age 25 is 45324. Find the number that attains age 26.

Describe intercensal and postcensal estimates of population growth assuming linear growth and exponential growth in mathematical method.

4.
Write a critical note on the salient features of Indian Censuses 199 J and 2001.

Explain Pearl and Read method of fitting logistic curve for population projection.
Find the missing values in the following table

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What is meant by fertility? How is it measured? Describe the various fertility rates commonly used. Discuss their relative merits.


5. A random variable has hazard rate at time t which is given by
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Derive the distribution function and survival function Calculate at
t 5 if α 2 λ

Define gamma distribution as a failure time model. Discuss the monotonicity property or its hazard rate.


Explain the log-rank test in a two-sample problem.

Which quality control processes are to be used by the data analysis centre to assess the data quality and to handle problems that are observed relating to data and data analysis?

Describe the general principles to be observed in preparation or Case-Report Form and the organization or the form.


6.
The survival times (in months) or 12 patients who have undergone a treatment are given below

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where denotes right censored observations.
Assuming that the survival times follow exponential distribution with mean 1/λ ,obtain the maximum likelihood estimate for the mean. Obtain the maximum likelihood estimate for
Compute at t 10 months.


The following data represents the survival times of extremely ill AIDS patients observed in days
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Compute Kaplan-Meier estimate of the survival function
Sketch the graph of against t. Compute and and compare.

Explain briefly the key categories of clinical trials data that are to be collected.

Explain, Phase I and Phase II clinical trials. What are MTD and DLT related to Phase I trials? Explain the traditional design approach used in Phase I trials.

Explain the basic differences among the chance and special causes of variation that affect process results.

State your agreement or disagreement to the statement given below, with brief justification:

"A statistically controlled process will always produce 100% results within tolerance limits."


Derive the control limits for the control chart for detects in a constant and varying number or sample units.



Explain the chart which describes the sensitivity or the sampling plan to detect the lot quality level for acceptance.

What is Cusum chart? Explain the methodology of using for process control.

8.
Evaluate the ARL to detect a a shift in the process average (no change in process variation) by one unit of standard deviation in the higher side assume use of X-chart with subgroup size 5 and probability of not detecting the shift is at most 0·05.

Explain the exponentially weighted moving average chart with at least one example of its potential application.

Describe the variable sampling scheme and compare it with the attribute sampling scheme.

An improvement in the process has resulted in increase or CPK from 0·6 to 0·95. Estimate the reduction in of nonconforming products. Assume the following Process average has not changed,
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and process is in statistical control.

9. In the ISS examination of a certain year, the distribution of scores in Statistics Papers II. III and lV is found to follow a 4-variate normal distribution with
known parameters. Indicate how you would estimate the percentage of candidates in that examination faring better Papers I and II compared to Papers III and IV, both in the aggregate, and in Paper I compared to Paper IV.

In multivariate analysis,often the issue of handling too many variables poses a big problem. How would you propose Lo solve the problem? Indicate the procedure.
Assuming the form of the conditional distribution of a subset X2, .... Xq) of random variables X2, ···, q following multivariate normal law for fixed values of (Xq+1.... derive the expression for the conditional mean of X1
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Define Fisher's linear discriminant function. Give a classifier rule for classifying an individual based on his or her measurements on p identified variables, into one of two mutually exclusive and exhaustive classes, clearly stating the underlying assumptions and explaining the notation you have used.
Show that in random sampling from a p-variate normal distribution, the sample variances and covariances follow Wishart distribution. Identify the

10.

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Define multiple correlation coefficient

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taken together,based on the observed set of data
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write down its expression.

Derive the simplified form of
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for the special case
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Derive the maximum likelihood estimators for the parameters of a multivariate normal distribution.

Discuss the procedure for testing the null hypothesis

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regarding the mean vectors of two multivariate normal distributions having


11. Discuss the usefulness of the principle of randomization in the context of design of experiments. Use the following set of random numbers to obtain the
layout of a randomized block design with 5 blocks of size 4 each for testing the treatments C and D


518 275 950 305 490 333 068 088 389 933 548 275
950 305 490 334 069 736 545 774 864 062 951 005

A 2^4 experiment has been laid out in 4 replicates in each replicate confounding one of the 3-factor interactions. Give the compositions of the 4 key blocks, and write down the ANOVA table.

What is a Latin Square Design? What are the main disadvantages of using such a design in field experiments? Indicate the procedure for obtaining the layout of a 5 X 5 Latin Square Design.

A 3^2 experiment with factors A and B each at levels 1 and 2 is to be designed in 2r replicates or 3 incomplete blocks each, such that in r replicates AB is confounded, while in the remaining AB^2 is confounded, the other-factorial effects remaining unconfounded in the entire design.
Give the layout of the 3 incomplete blocks of each of the two types of replicates, and write down the ANOVAtable.

The factor A has p levels which require relatively large experimental units.
Another factor B has q levels requiring relatively small experimental units. experiment. Discuss the procedure for testing the main effects A and as also
the interaction effect AB.

12.

It is desired to use a randomized block design with 4 blocks of size 6 each for testing the effects of 5 treatments D and E. In each block, treatments D and E are replicated once each, while treatment A is replicated twice to ensure more precise estimation and testing for A. Using a suitable model, give the expressions for different sums of squares,and write down the ANOVA table.
Discuss the procedures for testing equality of all treatment effects, as also for equality of effects of A and B. is the hypothesis of equality of all treatment effects is rejected.

A 3^3 factorial experiment with factors B and C each at levels 1 and 2 is to be laid out in 9 incomplete blocks of size 3 each, totally sacrificing information on the factorial effects ABC^2, AC^2 and AB^2c^2.
Give the layout or the design.
If this basic pattern is replicated r times, discuss the procedure for analyzing the experiment.

Discuss in detail, the procedure for analysis of covariance in a completely randomized design for testing the effects of t treatments with r1,r2,.....rt
replications respectively in the presence of just one concomitant variable.

A 2^3 experiment is proposed to be carried out in 2 incomplete blocks of size 4 each per replicate,retaining full information on all main effects and sacrificing equal amount of information on the remaining four factorial effects each. Suggest a scheme of partial confounding ensuring the above, and give the intrablock subgroup in each replicate.
Discuss the method of analysis for the data.

13. Write a C-program that will generate every nth integer, beginning with n start [i.e., i n start, n start n start+ 2n, etc.],ending with n stop. Calculate the
sum of those integers that are evenly divisible by some positive integer k.

Write a C-program to find whether a given matrix is a symmetric matrix and print the comment,


Write a C-program to calculate
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defining a recursive function and print it.


Write an R-program to fit a linear relationship of y on to get the summary of the relationship and to predict y for a given value of x.

Write an Reprogram to calculate the median of a set of observations.

14.
Write a C-program that will examine. each character in a line of text and determine how many of the characters are letters, how many are digits, how many are white space Characters, and how many are other kinds of characters
[e.g., punctuation characters) and print them.

Write a C-program to create a linear linked list, delete an existing component from the list defining suitable functions.

Write a C-program to evaluate where x and y are floating-point values and n can be an integer or floating point and print it.

Write a C-program to fit a normal distribution to a given observed frequency distribution and test for its goodness of fit and print the result,