Betting wheel. the wheel of fortune, we were betting on the wheel as a whole. Now imagine that you must bet on(invest in) individual segments of the wheel: 1. white, 2. black, or 3. gray with probabilities 1/2, 1/3, and 1/6, and payouts of $3, $2, and $6, respectively

a) Find the expected return r1_bar, r2_bar, and r3_bar for the three possible bets, b) Find the variances of returns for the three possible bets. Recall that variance is a measure of the degree of deviation from the mean. c) Calculate the covariances . Note: The expected value of the products such as E[r1r2] are all zero. Why? d) Calculate the correlations . Why are they negatively correlated to each other?