Think of two iid random variables $x$ and $y$ with density $f$ and CDF $F$ and a constant $c$. What could the qualitative meaning of the following expression be?
$$\iint_{-\infty}^{c+x}xf(x)f(y)dydx=\int x\left[\int_{-\infty}^{c+x}f(y)dy\right]f(x)dx=\int xF(c+x)f(x)dx$$
Any suggestion, including how to simplify this expression, will be appreciated!!
Let $A=[Y\lt X+c]$, then the integral is $\mathbb E(X\mathbf 1_A)$.