19. Suppose that W, the amount of moisture in the air on a given day, is a gamma random variable with parameters (t, B). That is, its density is f(w) = Be-Bw (Bw)/(t), w > 0. Suppose also that given that W = w, the number of accidents during that day-call it N-has a Poisson distribution with mean w. Show that the conditional distribution of W given that N = n is the gamma distribution with parameters (r + n, B+ 1).