1. Simulate 500 independent standard normal values. Use these to generate 250 pairs of bivariate normal vectors .Xi ; Yi / with zero means, unit standard deviations, and correlation 0.5. Find the average value of .Xi -Yi /2 over the simulations. Does it equal the theoretical average approximately?
2. (Use Your Computer). Simulate 500 independent standard normal values. Use these to generate 250 pairs of bivariate normal vectors .Xi ; Yi /, with zero means, unit standard deviations, and correlation p D :25; :5; :75. Use your sim- ulated pairs to estimate P.X > 0; Y > 0/. Does your estimate equal the theoretical value approximately?