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? e) Plot these three "investments" as a point on the graph of r_bar vs. for each of the investments . We plot the mean vs. the standard deviation rather than the mean vs. variance so that both axes have comparable units (such as percent per year). Comment on the relative risk vs. reward of the three choices