This question is totally independent of the previous questions. The joint probability density function $($PDF$)$ of $x$ and $Y$ is given by the

following function:

$y>0P(x>1|Y=y)E[x|Y=y]f_{x,Y}(x,y)=\{[e^{-(\frac{x}{y}+y)}{y}^{-1}if0$

For $y>0,$ find:

$A)P(x>1|Y=y)$;

$)E[x|Y=y].$

Written Answer:

Here use latex $to$ show all your intermediate analytical steps.