Calculate $E(Y | X = x)$

Question

Knowing that $f_{Y|X=x}=\frac{1}{x}$, where $x > 0$, I know have to calculate $E(Y | X = x)$. I have learned to do this by a simple integration operation like the following one: $$E(Y | X = x)= \int_0^{\infty}y \cdot f_{Y|X=x} \: dy=\int_0^{\infty}y \cdot \frac{1}{x}\:dy = \left[\frac{y^2}{2} \right]_ 0^{\infty}\cdot \frac{1}{x}$$ and this expression is divergent. How can I calculate the expected value then?

Answer 1

Okay I've understood know. It appears that $f_{Y|X=x}$ has a uniform distribution in $(0, x)$ so I just need to calculate this for a general $(a, b)$ interval and I get that the expected value is $\frac{x}{2}$