Toss a fair coin 3 times. Let X = the number of heads on the first toss, Y the total number of heads on the last two tosses, and Z the number of heads on the first two tosses. (a) Give the joint probability table for X and Y. Compute Cov(X. Y). (b) Give the joint probability table for X and Z. Compute Cov(X, Z).Let X be a random variable that takes values -2, -1, 0, 1, 2; each with probability 1/5. Let Y = X2. (a) Fill out the following table giving the joint frequency function for X and Y. Be sure to include the marginal probabilities. X -2 -1 0 1 2 total Y total (b) Find E(X) and E(Y). (c) Show X and Y are not independent. (d) Show Cov(X, Y) = 0. This is an example of uncorrelated but non-independent random variables. The reason this can happen is that correlation only measures the linear dependence between the two variables. In this case, X and Y are not at all linearly related