6. Let X be a discrete random variable with the following PMF

PX(k) = {0.4 for k = 1; 0.1 for k = 0; 0.3 for k = 1; 0.2 for k = 2}

Define a new random variable Y as Y = (X + 1)^(2).

(a) Find E(X)

(b) Find Var(X).

(c) Find the PMF of Y .

(d) Find E(Y ).