Let X be a random variable with range RX = {-1, 0, 1} and let P(X = 1) = P(X = -1) = p/2 for some p ∈ [0, 1].
a) Compute P(X = 0).
b) Compute the expectation E[X] and variance Var(X) of X as a function of p, and determine the value of p for which Var(X) becomes maximal.