Let X and Y have a bivariate standard normal distribution with correlation . Find P(X >0, Y > 0) by the following steps. Write X

Let X and Y have a bivariate standard normal distribution with correlation ρ. Find P(X >0, Y > 0) by the following steps.

Write X = Z₁ and Y = ρZ₁ +√1 − ρ²Z₂, where (Z₁, Z₂) are independent standard normal random variables. Rewrite the probability in terms of Z₁ and Z₂.