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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Sc.DEGREE EXAMINATION -STATISTICS
SECOND SEMESTER APRIL 2018
17/16UST2MC02 ST 2504 DISCRETE DISTRIBUTIONS
Date: 26-04-2018 Dept. No. Max. 100 Marks
Time: 01:00-04:00
PART A
Answer ALL the questions: (10X2=20 marks)
1. Define conditional expectation.
2. Explain moment generating function.
3. The mean and variance of binomial distribution are 4 and
3
4
respectively. Find
4. X is binomially distributed with the parameters n and p . What is the distribution of x
5. List any four application of Poisson distribution.
6. Under what condition Binomial tends to Poisson. Distribution.
7. Define Negative Binomial Distribution.
8. Write the expression for moment generating function of Geometric distribution.
9. Define trinomial distribution.
10. Write the expression for mean and variance of hypergeometric distribution.
PART B
Answer any FIVE questions: (5X8=40 marks)

12. Variate X and Y take the values 3 along with the probabilities shown below:
Y
X
1 2 3
1 k k k
2 k 2k k
3 k k k

13. State and prove any two properties of moment generating function.
14. Find the recurrence formula for Binomial distribution.
15. Derive the MGF of Poisson distribution. Find measure of Skewness and kurtosis.
16. Find the mean and variance of Negative Binomial Distribution.
17. Describe geometric distribution.
18. Explain multinomial distribution.
PART C
Answer any TWO questions: (2X20=40 marks)
19. Find the mode of Binomial distribution.
(ii).Obtain the recurrence relation for the central moments of Poisson distribution.
20. (i).Explain memory less property. Prove that Geometric distribution has this property.
(ii).Show that negative binomial distribution tends to Poisson distribution.
21. Derive the mean and variance of Hypergeometric distribution.
(ii).Derive the MGF of trinomial distribution and hence find mean and variance of X and Y.
22. The joint probability distribution of pair of random variables is given by
Y
X
1 2 3
1 0.1 0.1 0.2
2 0.2 0.3 0.1
Find Marginal distributions.
Evaluate conditional probability distribution of Y X 2.
Let X and Y be independent Poisson random variable with parameters respectively. Obtain
the distribution of
Marginal probability density function of X andY .
Covariance between X and Y .