X and Y are i.i.d with Uniform distribution in $[0,1]$. Let $M=XY$. What is the distribution of $X|M=1$ and $X|M=0$?
so, $M=XY$ and $U=Y$
$g_{1}(x,y)=xy$ and $g_{2}(x,y)=y$ $h_{1}=m/u$ and $h_{2}=u$
$J = 1/u$
So I will have: $f_{M,U}(m,u)=1/u$. Am I right?
To calculate $X|M=1$ I have to notice that $X = 1/y$
What I have to do is simply calculate the distribution o $1/Y$?
I got really confused here.
Any help?
Many thanks