\(X\) and \(Y\) have a joint probability density given by

\[f(x, y)=e^{-(x+y)}, \quad x \geq 0, y \geq 0\]

Find \(\operatorname{Pr}\{X \geq Y \geq 2\}\) and sketch the region in the \(x, y\) plane that defines the region of integration.