1. (a) Let U ~ Uniform[0, c] for some c > 0. Calculate E(Uk ) where k 2 0 is some fixed constant. (b) Let U and V be independent Uniform [0, 1] random variables. Calculate E(VU). (c) Let U ~ Uniform[0, 1] and suppose that, conditional on U, another random variable W is drawn from the Uniform [0, U] distribution. Calculate E(W) and Var(W)