We consider a random point $(X, Y)$ chosen with the following joiint density
$$f(x,y) =
\begin{cases}
\frac{1}{x^2y^2}, & \text{if } x \ge 1 \text{ and } y \ge 1 \\[2ex]
0, & \text{else}
\end{cases}$$
Consider another random variable Z=XY.
A. for $z \gt 1$ make a plot of the region in the $(x, y)$ plane given by
{$(x,y): xy \le z $} $\cap$ {$x \ge 1$} $\cap$ {$y \ge 1$}
B. Use the previous question to compute the cdf of Z.
For some reason I can't remember how to graph something that involves x and y, I decided to to get the equation in terms of x and then y and I got $y=\frac1x$ and $x=\frac1y$, but aren't these the same thing? is the answer to A. just the graph of $y=\frac1x$ starting from $x=1$ to $\infty$ and $y=1$ to $\infty$? I got the possible values of Z as $Z \ge 1$ if that helps, and I think X and Y are independent.
For B I think I know how to do the integration, but I just do not know how to set it up?
Wolfram Alpha gives us bounds. Try changing 2 with different numbers $>1$ here.
So we have
$$F_Z(z) = P(Y - \frac{z}{X} \le 0) = \int_1^z \int_1^{z/x} \frac{1}{x^2y^2}dydx$$