1. (Bivariate Normal Probability). Suppose the amounts of oil (in barrels) lifted on a given day from two wells are jointly bivariate normal, with means 150 and 200, variances 100 and 25, and correlation .5. What is the probabil- ity that the total amount lifted is larger than 400 barrels on any given day? What is he probability that the amounts lifted from the two wells on any day differ by more than 50 barrels?
2. (Conceptual). Suppose .X; Y / have a bivariate normal distribu- tion with zero means, unit standard deviations, and correlation p; -1 p 1: What is the joint distribution of .X C Y; X - Y; Y /? Does this joint distribution have a density?