2. Inverse Transform Sampling: Let F be a cumulative distribution function (CDF) that is strictly monotonic increasing (so its inverse F'l exists). Let U be a uniform (0,1) random variable. ' a) If X :2 F_1(U) show that X has cumulative distribution function F. ' b) Show mathematically that sampling U and taking values of 10g(U) mimics sampling an exponential random variable with mean 1. (Note: To derive these results requires using results for functions of random variables that you hopefully have seen but they are also reviewed in Ross Chapter 2; he gives the formulas for multivariate distributions and this is a simpler case)