Suppose that W, the amount of moisture in the air on a given day, is a gamma random variable with parameters

Suppose also that given that , the number of accidents during that day - call it N - has a poisson distribution with mean .

Show that the conditional distribution of W given that N = n is the gamma distribution with parameters

I would like some help to write the formula for the second supposition, as it goes from a continuous rv to a discrete one

Thanks