the question asks for the density of the smaller of $X$ and $Y^3$, $X$ and $Y$ both being exponentially distributed independent random variables with densities $ae^{-ax}$. I think I know that I have to start by finding $P(X = x, Y^3 > x) + P(Y^3 = x, X>x)$, and then integrate from $x$ to $\infty$. I'm not sure where to go from here.
Thanks!