Let X be a discrete random variable that takes values X()={2,1,0,1,2}, and suppose that X has probability mass function pX(x) = c(1 + x^2) for x X(), where c is a positive constant.

(a) Find the value of c.

(b) Find the expectation of X.

(c) Let Y = |X|. Find the PMF of Y.

(d) Compute E[Y]using the PMF of Y.

(e) Compute E[Y] again a different way by using Theorem 3.4(i) in Probability for Data Science.