Lt A and L denote the area and perimeter of a rectangle with length $X$ and height $Y$, such that $X$ and $Y$ are independent, and uniformly distributed on $(0,1)$. Find the density function of $A$ and $L$.
Will it just be $$f(x,y) = 2xy(x+y)$$
The above is just my guess and likely wrong, because when I use it to calculate $\mathbb{E}(A)$ and $\mathbb{E}(L)$ , I get the wrong values, so what will be the distribution function?
