I am doing some problems from a practice final and would like to know if the following problem has mistakes in the way it is written. We are supposed to apply a corollary that doesn't seem to have any relevance in this context. It is throwing me off.

Problem statement: Suppose that and and they are independent. Let and . Use the following corollary to find the marginal distributions of $X$ and $Y$.

Corollary: Let be mutually independent random variables with . Let and be fixed constants Then

.

Also, aren't the marginal distributions of $X$ and $Y$ just $X$ and $Y$ themselves, because they are independent of each other??

Any help would be greatly appreciated. My final is tomorrow and I'm studying as hard as I can.