Suppose that a discrete random variable X has range {−4,−3,−2,−1, 0, 1, 2, 3, 4}

and the following probability function

(i) Show that the random variable Y = |X| has probability function

(ii) Find the expectation for each of the variables X and Y and examine whether |E(X)| = E(|X|).

fx(x) = x = 0, x+1, 12, 13, 14. = 10