Question 4 Suppose that X and Y are independent discrete random variables having Poisson /11 distributions with parameters A, > 0 and > >:0, respectively. (a) Explain why P(X + Y = =) = >P(X = z, Y = :-I). /2 (b) Prove that X + Y has a Poisson distribution with parameter ), + 12- /5 Page 9 of 14 9/14 (c) Find the conditional probability of X given X + V. That is, P(X = = [ X+V = =). Identify the conditional probability in terms of a discrete probability distribution. You may assume that ( a + b)" = > ( ) * *