Let N be a Poisson() random variable. We observe N, say it equals n, we then throw a p-biased coin n times and let X be the number of heads we get. Show that X is a Poisson(p) random variable. (You can use the following identity: k=0 y^k / k! = e^y

4. Let N be a Poisson (1) random variable. We observe N, say it equals n, we then throw a p-biased coin n times and let X be the number of heads we get. Show that X is a Poisson (pA) random variable. (You can use the following identity: EX-o k! = ey.)