Let (X, Y) have a bivariate normal distribution with parameters E(X) —3, E(Y) = 10...

1. Let (X, Y) have a bivariate normal distribution with parameters E(X) —3, E(Y) = 10, var (X) = 25, var(Y) = 9 and corr(X, Y) = 0.6. Determine (a) P(7 2. Suppose that Y ti N(0,1) and X1Y = y ti N(a 13y, Q2). Without initially as-suming that (X, Y) are bivariate normal. find the means, variances and correlation of X and Y. Hint: you will need to use the iterated expectation and variance formulae. Write down the bivariate normal density that has these parameters and compare this with the joint density of X and Y obtained from the above distributions. Hence deduce that (X, Y) has a bivariate normal distribution. 5. Let (X, Y) have the bivariate probability density function