Let Y be the rate (calls per hour) at which calls arrive at a switchboard. Let X

Question:

Let Y be the rate (calls per hour) at which calls arrive at a switchboard. Let X be the number of calls during a two-hour period. A popular choice of joint p.f./p.d.f. for (X, Y) in this example would be one like

a. Verify that f is a joint p.f./p.d.f. Hint: First, sum over the x values using the well-known formula for the power series expansion of e2y.
b. Find Pr(X = 0).