Question: Problem 1.1 (10 points) Suppose X and Y are two discrete random variables with joint proba- bility mass function px,y(c, y) whose values are given

Problem 1.1 (10 points) Suppose X and Y are two discrete random variables with joint proba- bility mass function px,y(c, y) whose values are given in the table below: 1 2 1/4 0 0 1/2 1/12 1/6 (a) Compute E[X], E[Y], Var(X), Var(Y) and Cov(X, Y). (b) Let Z = (X + Y)/2. Compute E[Z], Var(Z) and Cov(X, Z)

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