The probability function of a discrete random variable X has the form f (x) = c(x2 + 2|x| + 1), x ∈ RX = {−2,−1, 0, 1, 2}, for a suitable constant c.
(i) Find the value of c.
(ii) Calculate E(X) and then find the expectation of the random variables Y = |X|
and W = 5X − 3|X|.