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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)

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.

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