Three people toss a fair coin and the odd one pays for coffee. If the coins all turn up the same, they are tossed again. Find the probability that fewer than 4 tosses are needed. Let X, Y be two discrete random variables and let p(x, y) = P(X = x, Y = y) be their joint probability mass function with p(0, 0) = 0.3, p(0, 1) = 0.2, p(1, 0) = 0.13, p(1, 1) = 0.37 (a) Are X and Y independent? Why? (b) Find E[X + Y] (c) Find Var(X + Y) (d) Find E[Z), where Z = max (X, Y)