Math Help - hello. i need help on this problem on joint probabiltiy

1. hello. i need help on this problem on joint probabiltiy

prove that X and Y are independent if and only if fx|y(x|y)= fx (x) for all x and y.

2. Re: hello. i need help on this problem on joint probabiltiy

$f_{X|Y}(x|y)=\frac{f_{X,Y}(x,y)}{f_Y(y)}$

$X$ and $Y$ independent $\implies f_{X,Y}(x, y)=f_X(x)f_Y(y)$