4. [7 points] Let the random variable X have distribution function ff_x}=w._ sen g e (a) |2 points] Compute E[X]. (b) [2 points] Compute var(X ). (c) [3 points] Compute E[3X?2 2X + 4] and var(2X + 4) 5. [9 points] Let X be a random variable such that PX=1)=pand P(X =-1)=1-p. Let be a random variable which is independent of X and with the same probability distribution, that is P=1)=pand P(=-1)=1-p. Define = X. (a) [4 points] Determine the probability distribution of random variable Y. (b) |3 points] Assume that p = ;, are X and Y independent? Explain your answer. (c) [2 points] Assume that p # %, are X and Y independent? Explain your