MAY 2018 Sub. Code: 2861
M.Sc. BIOSTATISTICS EXAMS
FIRST YEAR
(New Regulation)
PAPER I PROBABILITY AND DISTRIBUTION THEORY
Q.P. Code: 282861
Time: Three hours Maximum: 100 Marks
I. Elaborate on: x 20 40)
1. Derive the marginal and conditional distribution of X and Y in a bivariate
normal distribution.
Define expectation. State and prove all properties of expectation.
2. Eight coins are tossed at a time 256 times. Number of heads observed at each
throw is recorded and the results are given below. Find the expected frequencies.
What are 17 40 20 the theoretical values of mean and standard deviation?
Calculate also the mean and SD of observed frequencies. No. of heads at throw:
0 1 2 3 4 5 6 7 8 Frequency 2 6 30 52 67 56 32 10 1.
II. Write notes on: (10 x 6 60)
1. Bivariate and multivariate normal distribution.
2. Mahalanobis D2 statistic.
3. Cochran's theorem.
4. Logistic distribution.
5. Holders Inequality.
6. Characteristic functions.
7. If X and Y are independent random variables show that and function of
X and Y is also independent. Is the converse true.
8. Mahalanobis D2 and its relation with T2 statistic.
9. Mean and variance of Hypergeometric distribution.
10. Minkowski inequalities.