My joint PDF function of (x,y) is given
\begin{cases} 2e^{-x-y}, & 0\leq x\leq y\leq \infty\\0, & otherwise
\end{cases}
How do I find joint CDF from this PDF? I know that my CDF is zero when both x and y are less then zero and that I'm supposed to integrate PDF on a given region, but there is a solution in my book that says I'm supposed to calculate CDF on this area too:
$$ 0\leq y\leq x, y>0 $$
and it equals $$e^{-2y} - 1$$
Why do I do this? Shouldn't CDF be zero in this case? Also, isn't it redudant to say that y>0 in that area?
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