compute marginal I have tried to solve this exercise
Let $X$ and $Y$ be random variables with joint probability density function
given by: $f(x,y)=\frac{1}{8}(x^2-y^2)e^{-x}$ if $x>0$, $|y|<x$
Calculate $E(X\mid Y=1)$
so, the marginal $f_Y(y)$ is $\int_y^\infty \frac{1}{8}(x^2-y^2)e^{-x} dx +\int_{-y}^\infty \frac{1}{8}(x^2-y^2)e^{-x} dx\ $ ?
Is correct?

$$
\text{What you need for the marginal is }
\begin{cases} \displaystyle \int_y^\infty & \text{if } y\ge 0, \\[10pt]
\displaystyle \int_{-y}^\infty & \text{if } y<0.  \end{cases}
$$
Or you can just write it as $\displaystyle \int_{|y|}^\infty\!\!.~~$  At any rate in $f_{Y=1}(y)$ you'd have $\displaystyle\int_1^\infty$.
