Let X,..., X be independent with P{X; = 1} = P = 1 - P{X, = 0}, i = 1, n. Show that X, Bin(n,p), 1=1 where Bin(n, ) is a binomial random variable with parameters n and Pln. (Hint Prove it first for n = 2.) Use the above to show X, Y, where Y is Poisson with mean np. Hence, for instance, a Poisson random variable is more variable than a binomial having the same mean. that =