I'm unsure of how to find the joint PDF of something like this
Assume that X1, X2 is uniform on the square with corners (-1,0), (0, —1), (0, l), (1,0)
I know that it is double integration with bounds [-1, 1] for x and [-1, 1] for y. However, what am I integrating?
The joint density is given by $f(x,y)=\frac 1 4$ for $-1 \leq x \leq 1,-1 \leq x \leq 1$ (0 elsewhere). The distribution function is $F(x,y)=\frac 1 4 \int_{-1}^{x} \int_{-1}^{y} d xdy=\frac 1 4 (x+1)(y+1)$ for $x,y \in [-1,1]$. It is $\frac 1 4 \int_{-1}^{x} \int_{-1}^{1} d xdy=\frac 1 2 (x+1)$ for $x \in [-1,1], y>1$ etc.