I have a density function $g(x,y)=4xy \mathbb{I}_{[0,1]\times[0,1] }(x,y)$. How can I get a distribution function $G(x,y)$?
I found that $G(x,y)= \int _{-\infty}^x \int _{-\infty}^y f(u,v) du dv$ where $f(u,v)$ is density function and $G(x,y)$ distribution function. I this right? How can I use it
$G(x,y)=\int_0^{x}\int_0^{y} 4uv du dv=x^{2}y^{2}$ for $0\leq x,y \leq 1$. For $0\leq x \leq 1$ and $y >1$ we have $G(x,y)=\int_0^{x}\int_0^{1} 4uv du dv=x^{2}$ and for $0\leq y \leq 1$ and $x >1$ we have $G(x,y)=y^{2}$. Finally $G(x,y) =1$ if $x,y >1$ and $0$ of $x,y<0$.