We're learning about independent random variables in the context of multivariate probability distributions and I just need some help with this one question.
If $f(y_1, y_2)=6y_1^2y_2$ when $0\leq y_1 \leq y_2, y_1+y_2\leq 2$ and $0$ elsewhere
Show that $Y_1$ and $Y_2$ are dependent random variables.
The real problem I'm having with this question I've realized, is that I don't really understand how to get the marginal densities of Y1 and Y2. If someone could walk me through that, it would be greatly appreciated!