We have this density are asked to verify if the double integral over $R^2$ of the density evaluates to $1$ (the second part of the problem asks to find the expectation of $X$). The density given is $f(x,y) = \frac35(5 - 3x - 2y), 0 < x + y < 1$, and $0$ otherwise.
I am having some trouble setting up the bounds of integration. I tried to sketch a graph which is simply two parallel lines, the first: $y = 1 -x$, the second: $y = -x$. So we are interested in integrating over the region enclosed by the two parallel lines. Therefore, I setup the following integral:
$1 = \int_{-\infty}^{\infty}\int_x^{1-x}f(x,y)dydx$. But this integral does not converge. So either I have the wrong bounds for my integrals or am going wrong somewhere else, but not sure where. Looking for some hint on how to proceed.