Let X and Y be independent Poisson random variables with rates 1 = 2 and 2 = 3,

respectively.

(a)Find the joint PMF of X and Y , e.g. find the function that stands for

p(x,y)=P(X=xand Y =y).

What are the possible values for x and y and what are the values of p(x,y)?

Write the probabilities down as a function of x and y.

(b)Find the probability that X + Y 1.

(c)Obtain the general PMF for the random variable X + Y .