I proved that here last week.....
2.Suppose that Y1 and Y2 are independent Poisson distributed random variables with means lambda1 and lambda2, respectively. Let W = Y1 + Y2. Assume that we had shown that W has a Poisson distribution with mean lambda1 + lambda2. Use this result to show that the conditional distribution of Y1, given that W = w , is a binomial distribution with n=w and p = (lambda1)/(lambda1 + lambda2)
Please help, thanks for your time