# Thread: Transformations of standard normal variables

1. ## Transformations of standard normal variables

Suppose that $X$ and $Y$ are independent standard normal random variables ~ N(0, 1).

What are the distributions of the following transformations?
1. $\frac{X^{2} - Y^{2}}{\sqrt{X^2 + Y^2}}$

2. $\frac{2XY}{\sqrt{X^2 + Y^2}}$

Are they independent?