Suppose that a discrete random variable X has probability function f (x) = P(X = x) = 1 5, x ∈ RX = {−2a,−a, 0,

a, 2a}.

(i) Show that, regardless of the value of

a, we have E(X) = 0.

(ii) Calculate Var(X) as a function of

a. What happens with the variance as a increases? Give an intuitive interpretation of this result.