9. Let X be a random variable with probability generating function P(s) =Pks. What is k the probability Y = 2X ? generating function of (a) P(√s) + P(-√s) P(√s) - P(- √s) (b) 2 (c) P(√)-P(-√s) P(√s) + P(-√s) (d) 2 10. A simple random sample of size 10 is selected with replacement from a population of size 100. What is the expected number of unique elements in the sample? 10 99 (a) 100x 100 10 99 (b) 100x 100 10 9 (c) 100x 10 10 99 (d) 100x 1 100 2 B-GSE-P-TUA 12. (3-A 8. Let X be a Poisson variate with parameter à such that P(X = 2) = 2P(X = 4)+ 20P(X = 6). What is the coefficient of skewness? 1 (a) මපිමලි √3 (b) 1 (c) (d) √3 12 11 with probability 6. A Poisson variable X has mean equal to 2 Consider the following for Y = 2X: E(Y) = 1 = 1 2. Var(Y)=4 3. H3(Y) = 4 4. 114(Y) = 28 Which of the above is/are correct? (a) 1 only (b) 2 and 4 only (c) 1 and 3 only (d) 1, 2 and 3 only 7. Let the random variable X have the distribution P(X = 0) = P(X = 3) = p, P(X = 1) 1-3p for 0 ≤ p ≤ 1/2. What is the maximum value of V(X)? (a) 3. (b) 4 (c) 5 (d) 6