Let X and Y be two independent random variables. Given the marginal pdfs shown below, find the

Question:

Let X and Y be two independent random variables. Given the marginal pdfs shown below, find the pdf of X + Y. In each case, check to see if X + Y belongs to the same family of pdfs as do X and Y.
(a) pX(k) = e−λ λk/k! and pY(k) = e−μ μk/k! , k = 0, 1, 2, . . .
(b) pX(k) = pY(k) = (1 − p)k−1 p, k = 1, 2, . . .