# Math Help - Finding a density function.

1. ## Finding a density function.

A friend of mine was asking me for help with this exercise, and I'm not sure how to tackle it, could someone please help me.

a) We are given a density function for the random variables $Y_1$ and $Y_2$
$f(y_1 , y_2)=\begin{cases} e^{-y_1} &\quad\text{ if }\quad 0\leq y_2 \leq y_2 \leq \infty \\ 0 &\text{elsewhere}\end{cases}$

Now we are given a new random variable $U=Y_1 - Y_2$, and we need to find the density function for U.

b) Find $\mathbb{E}[U]$ and $\mathbb{V}[U]$

I could appreciate some help, I have not yet studied integrals in multiple variables, but I'm not sure if I have to do that for this problem.

2. You can either obtain the CDF or transform to U and W, where W is any other variable you wish.
However, all of this assumes you've seen multivariate calculus.