6. Two questions (10 points). A contestant is presented with two questions, Q1 and Q2. If she decides to answer Q5, 73 E {1, 2} rst, then she is allowed to move to the other question only if her answer to Qz- is correct. Let the probability that the contestant answers Q1 correctly be p1 = 0.6 and the payoff for correct answer be c1 =$2; and the probability that she answers Q2 correctly be p2 = 0.1 and the payoff be c2 =$1. Assume that the events of answering Q1 and Q2 correctly are independent. Let Xi, i E {1, 2}, be the payoff if the contestant chooses Qi first. (a) Which question should she try to answer first in order to maximize her expected payoff? (b) Find Var(X1) and Var(X2) and comment on the choice of part (a)