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. Suppose that the marginal p.d.f. of Y is

and that the conditional p.f. of X given Y = y is

a. Find the marginal p.f. of X. (You may use the formula
b. Find the conditional p.d.f. g2(y|0) of Y given X = 0.
c. Find the conditional p.d.f. g2(y|1) of Y given X = 1.
d. For what values of y is g2(y|1) > g2(y|0)? Does this agree with the intuition that the more calls you see, the higher you should think the rate is?