This problem has been irritating me for a couple days now. I can't figure it out.

The only part I really need help with is determining the joint pdf. I can figure out the rest, given what the pdf is. I would appreciate any input!!!Let $\displaystyle X_1,\,X_2$ denote a random sample from a distribution $\displaystyle \chi^2\left(2\right)$. Find the joint pdf of $\displaystyle Y_1=X_1$ and $\displaystyle Y_2=X_1+X_2$. Note that the support of $\displaystyle Y_1,\,Y_2$ is $\displaystyle 0<y_1<y_2<\infty$. Also find the marginal pdf of each $\displaystyle Y_1$ and $\displaystyle Y_2$. Are $\displaystyle Y_1$ and $\displaystyle Y_2$ independent?