1. Let Xi = poisson (lamda i) (i = 1,....n) be independent random variables and let N = sum Xi. show that X|N = n~Muliomial (n, p1, p2...pk) with pi = lamda i / (sum lamda i, i =1 to k)

2. Let {Xi} i=o to infinity and Y independent radom variables. Suppose that Xi ~Binomial (1,p) and Y ~ Poisson (lamda) Calculate the mean and variacen of S= sum Xi (i=1 to Y)