exponential, gamma,and poisson problem in one!

[pete2323]

I think your allowed to consider a gamma with alpha = 2 as 2 indepent exponentials correct?

[pete2323]

Can someone help me with this problem? My functions are f (m)= e^-2m because it is a gamma with alpha of 2 and beta of 1. and f (x given m)= (m^x*e^-m)/x!



How do you get f(x) to solve the problem?



The problem is: Let x have a Poisson distribution with mean m, and m is an experimental value of a random variable with gamma distribution with alpha=2 and beta=1

Calculate px is <= 2 ?