1. Consider the Monte Carlo approximation of a mean for a generic random variable: . um = 1 m Xi where Xi ~f(.). Let u and o be the common mean and variance of the Xi, (i.e., E[Xi] = / and Var [Xi] = 02 for all i). . a) Derive Var ( Um ) in terms of u, , and m as needed. . b) Using similar logic, derive a Monte Carlo approximation of o that you will label o . Take advantage of the identity Var ( X ) = E[X2] - E[X]2. . c) Using your previous two results, provide a way of approximationg the variance of your Monte Carlo estimator Um