Let X and Y be two independent random variables. Assume that Xis Negative-
Binomial(2, θ) and Y is Negative-Binomial(3, θ) distributed. Let Zbe another random
variable, Z = X + Y .
(a) Find the following probabilities: P(Z = 0), P(Z = 1) and P(Z =2);
(b) Can you guess what is the distribution of Z?
