Let X and Y have a bivariate standard normal distribution with correlation ρ = 0. That is, X and Y are independent. Let (x, y) be a point in the plane. The rotation of (x, y) about the origin by angle θ gives the point
![](https://test.transtutors.com/qimg/5b734f2a-70a1-4e63-a46e-f3f61261ddb0.png)
Show that the joint density of X and Y has rotational symmetry about the origin. That is, show that f(x, y) = f(u, v).