Problem 1. Consider an experiment with three possible outcomes 1, 2, 3. For each i = 1, 2,3 let wager i be the bet on outcome i. Suppose that the return of the bet on wager i is either $o; if i is the outcome of the experiment or $1 if i is not the outcome. Outcome i 1 2 3 Odds oj 1 2 5 (a) Suppose that the outcome j occurs with probability Pj, where p = P2 = P3 = 1/3. Find the expected return of the three wagers. (b). Find a probability p= (P1, P2, P3) such that the returns of the wagers are all zero. Hint: the answer is p= (1/2, 1/3, 1/6). Problem 2. Consider an experiment with three possible outcomes 1, 2, 3. For each i = 1, 2,3 let wager i be the bet on outcome i. Suppose that the return of the bet on wager i is either $o; if i is the outcome of the experiment or -$1 if i is not the outcome. Odds oj Outcome j 1 2 3 3 4 4 Consider the strategy (x1, 12, 13) = (3,2,2). That is, bet $3 on wager 1, $2 on wager 2, and $2 on wager 3. Calculate the return of this strategy. Is this an arbitrage? Problem 1. Consider an experiment with three possible outcomes 1, 2, 3. For each i = 1, 2,3 let wager i be the bet on outcome i. Suppose that the return of the bet on wager i is either $o; if i is the outcome of the experiment or $1 if i is not the outcome. Outcome i 1 2 3 Odds oj 1 2 5 (a) Suppose that the outcome j occurs with probability Pj, where p = P2 = P3 = 1/3. Find the expected return of the three wagers. (b). Find a probability p= (P1, P2, P3) such that the returns of the wagers are all zero. Hint: the answer is p= (1/2, 1/3, 1/6). Problem 2. Consider an experiment with three possible outcomes 1, 2, 3. For each i = 1, 2,3 let wager i be the bet on outcome i. Suppose that the return of the bet on wager i is either $o; if i is the outcome of the experiment or -$1 if i is not the outcome. Odds oj Outcome j 1 2 3 3 4 4 Consider the strategy (x1, 12, 13) = (3,2,2). That is, bet $3 on wager 1, $2 on wager 2, and $2 on wager 3. Calculate the return of this strategy. Is this an arbitrage