The probability function of a discrete random variable is given by f (x) = c(32 − x), x = 1, 2,…, 31, where c is a constant.

(i) Show that c = 1∕496.

(ii) Find the expectation E(X).

(iii) Find the expectation of the random variable Y = 3(X − 11) and show that Var(Y) = E(Y2).