Let (X1, X2) have the bivariate normal distribution with both means equal to 0, both variances equal to 1, and the correlation equal to 0 5 We wish to estimate Pr(X1 2, X2 1) using simulation a Simulate a sample of 10,000 bivariate normal vectors with the above distribution Use the proportion of ve...

a We can simulate bivariate normals by simulating one of the marginals fir ...

Let (X1, X2) have the bivariate normal distribution with both means equal to 0, both variances equal

Question:

Let (X1, X2) have the bivariate normal with both means equal to 0, both variances equal to 1, and the correlation equal to 0.5. We wish to estimate θ = Pr(X1 ≤ 2, X2 ≤ 1) using simulation.
a. Simulate a sample of 10,000 bivariate normal vectors with the above Use the proportion of vectors satisfying the two inequalities X1 ≤ 2 and X2 ≤ 1 as the estimator Z of θ. Also compute the simulation standard error of Z.
b. Use the method described in Example 12.4.3 with 10,000 simulations to produce an alternative estimator Z' of θ. Compute the simulation standard error of Z' and compare Z' to the estimate in part (a).
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...