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Suppose a discrete random variable X has the following probability distribution: X -2 -1 O 2 P(X) 0.2 0.3 0.15 0.2 0.15 (a) Find the mean of X and E[X2]. (b) Find the probability distribution for Y" = 2X2 + 2. Provide a table with Y and P(Y). (c) Find E |Y ] using your answer from part (b). (d) Now use part (a) to find E [Y].Suppose a discrete random variable X has the following probability distribution: X 2 3 P(X) 0.2 0.4 0.15 0.25 (a) Find the probability distribution for Y = 3X - 2x + 1. Provide a table. (b) Find E [Y] using your answer from part (a). (c) Find E [X] and E[X2]. (d) Find P(Y 0). (d) Are X and Y independent