Exercise 5 (4 + 4 points). Let (X1, . . . , X\") denote a random vector. Let g : IR" % R be a function. 1. Show that E(ag(X1, . . . ,Xn) + b): aE(g(X1, . . . ,Xn)) + b . You should have two different proofs, one for the case when X is a discrete random vector and the second for when X is a continuous random vector. Please also explain in words what this result says. 2. If a g 9(X1, . . . ,Xn) g b, show that a S E(g(X1, . . . ,Xn)) S 1). Please also explain in words what this result says. Now let 9(321, . . . ,mn) : maxlgign 3:1- and let (X1, . . . , X") denote a random vector where each coordinate Xi E [0, l] with probability 1. Show that E (9(X1, . . . ,Xn)) is bounded between 0 and 1