Suppose that X and Y are independent, that X has the beta
Chapter 12, Problem 6(choose chapter or problem)
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.
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