(4) Solve the following problems about a variance. (a) [1pt] Starting from Var(X) = E[(X -E(X))'], prove that Var(X) = E[X?] - [EX] for any random variable X. (b) [1pt] Using the result of (a), prove that E[X?] 2 [EX] for any random variable X. (c) [1pt] For any random variable X and any constant a, be R, prove that Var(ax + b) = a? Var(X) I -2 -1 0 1 2 (d) [1pt] Let X have the distribution given by P(X = x) 0.3 0.1 0.2 0.1 0.3 What is SD(X)? (e) [Ipt] Use the same X as in (d). What is SD(|XI)