J 2

A Pizza shop has N customers per day, where N is random with Poissonoge 5). The ith customer (i = 1,.. .,N) buys Xi Pizzas, and X;- has the PMF p(x) = c(0.8)x/x, x = 1,2,3,... N,X1,X2,... are all mutually independent. Derive the PMF of T, which is the total number of Pizza sold in a day. Find the mean and variance of T