Suppose that X and Y are independent, that X has the beta distribution with parameters 3.5 and 2.7, and that Y has the beta distribution with parameters 1.8 and 4.2. We are interested in the mean of X/(X + Y).You may assume that you have the ability to simulate as many random variables with whatever beta distributions you wish.
a. Describe a simulation plan that will produce a good estimator of the mean of X/(X + Y) if enough simulations are performed.
b. Suppose that you want to be 98 percent confident that your estimator is no more than 0.01 away from the actual value of E[X/(X + Y)]. Describe how you would determine an appropriate size for the simulation.