If two random variable have the joint density given by
$\displaystyle f(x,y) = \begin{cases} 2e^{-2y} e^{-x} & 0<x< \infty , o<y<\infty\\
0 & otherwise \end{cases}$
Are X and Y independent ?
You have been told how to do this. You are expected to have sufficient understanding of things so that explanations such as those given make sense.
Go back to your textbook or class notes and review this material. Also, click on 5.2 here: Probability density function - Wikipedia, the free encyclopedia