I have searched for this question, however, they only give the definition of joint pdf $\iint f(x,y)dxdy =1$ and examples like: $f(x,y)=x+cy^2, 0\le x\le 1, 0\le y\le 1$ find $c$.
But not for how to derive $f(x,y)$ from $f(x)$ and $f(y)$.
I want to know, for example, how to derive a joint pdf $f(x,y)$ of $2$ random variables $X, Y$ from a gamma distribution or from any $2$ distributions?
Hope I can have a calculation example for this, and a website reference for explaining how this can be done would be great. Thanks.
It is not possible to find the joint density $f(x,y)$ from $f_X$ and $f_Y$ in general. When $X$ and $Y$ are independent $f(x,y)=f_X(x)f_Y(y)$.