Please solve all parts

1 1. Toss a coin 3 independent times where P(H) = E on each toss. Let X = number of heads out of the three tosses, Y = number of heads out of the rst two tosses, and Z = number of heads on the last toss. (vi) Find the joint probability distribution of X and Y, C'oi)(X, Y), and Corr(X, Y). (vii) Find the joint probability distribution of X and Z, Cov(X , Z ), and COTT(X, Z). (viii) Find the joint probability distribution of Y and Z, Cov(Y, Z), and Corr(Y, )