Question: Let X and Y be independent random variables with X having the t distribution with five degrees of freedom and Y having the t distribution

Let X and Y be independent random variables with X having the t distribution with five degrees of freedom and Y having the t distribution with three degrees of freedom. We are interested in E(|X − Y |).
a. Simulate 1000 pairs of (Xi, Yi) each with the above joint distribution and estimate E(|X − Y |).
b. Use your 1000 simulated pairs to estimate the variance of |X − Y | also.
c. Based on your estimated variance, how many simulations would you need to be 99 percent confident that your estimator of E(|X − Y|) is within 0.01 of the actual mean?

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