1. Define X = VU, where U ~ Unif(0, 1). (a) (3 points) Compute probability density function (pdf) f(X). a) (3 points) Compute E(X). (b) (3 points) Compute var (X). (c) (3 points) Use R to generate a realization of 5000 independent copies of X and produce a histogram of these realizations. (d) (3 points) Using the data generated in part 1c, compute a simulation- based estimate of E(X). Is this estimate close to the actual value computed in part la