My homework problem asks me to determine if the random variables $X$ and $Y$ are statistically independent, given their joint density function:
This is only true if $f(x,y) = f_X(x)f_Y(y)$, where the subscripted functions are the marginal distributions of $X$ and $Y$, respectively. Here is a screenshot of my work in MS Word:
Part of me suspects this is wrong. Is my work correct? If so, please don't tell me the correct steps to take. Rather, offer some hints to push me in the right direction so I can solve it on my own. Thank you! :)