Let X be a binomial random variable with Pr(X = x) = (n/r)pXqn-x, x - 0, 1

Question:

Let X be a binomial random variable with Pr(X = x) = (n/r)pXqn-x, x - 0, 1 2, . . ., n, where n (> 2) is the number of Bernoulli trials, p is the probability of success for each trial, ad q = 1 - p.
(a) Show that E(X(X - 1)) = n2p2 - np2.
(b) Using the fact that E(X(X - 1)) = E(X2 - X) = E(X2) - E(X) and that E(X) = np, show that Var(X) = npq.