2 Suppose that X Y have a bivariate normal distribution with

2. Suppose that (X, Y) have a bivariate normal distribution with parameters (5,3, 1,4, 0.5). Compute the following quantities:

Solution

We are given the parameters mux = 5, muy = 3, sigma x = 1, sigma y = 4 and row = 0.5

a) P(Y>6) = P(6 < Y < ?) = 0.226

b)P(6.5 < X < 6.5 ? -? < Y< ?) = 0.0000

c) P(Y>6/x=6.5) =  0.001