B1. (a) Let X ~ Bin(n, p). By using the formula EX = Σxpx(x), x Show that EX = np. You may use the binomial expansion, Hint: First show that m Σπ agm-k (a+b)m = Σ k=0 (m) (+-) - (2)² }) (b) Let X and Y be random variables, and let a be a constant. Starting from the definition of covariance, show that Cov(aX,Y) = a Cov(X, Y). (c) Let X and Y be Bernoulli ( ✓ ✓) random variables. Write down a table for the joint PMF of X and Y for which X and Y are uncorrelated.