# Probability distribution function with arctan

1. Dec 15, 2008

### aus_fas

Hi I have a function $$\phi =arctan(Y/X)$$ where, X$$\sim \mathcal{N}(A\cos \theta, v)$$ and Y$$\sim \mathcal{N}(A\sin \theta,v)$$. I want to find
pdf (probability distribution) of $$\phi$$. Any suggestions ? I think change of variables in integral might work??

2. Dec 16, 2008

### rochfor1

There's a change of variables formula for two r.v.s for situations like this. It amounts to changing variables in the integral of the joint pdf.

3. Dec 17, 2008

Thanks,