Let $f(x,y)=1/2$ in square with vertices $(1,0),(0,1),(-1,0),(0,-1)$

Question

This problem is from Rohatgi's introduction to probabilities:

Let $(X,Y)$ have joint PDF defined as $f(x,y)=1/2$ on square with vertices $(1,0),(0,1),(-1,0),(0,-1)$. Find marginal PDFS of $X$ and $Y$.

From my understanding, the PDF that is given is not a proper PDF since it integrates to $2$ over the given bounds?

Answer 1

Check your square. It looks like this:

The square has area $2$ so the pdf given is accurate. Marginal pdfs are triangular in form.