Expectation of a uniform distribution

Question

$X$ is uniform over $(0,1)$. What is $E[X|X<\frac12]$?

Here's what I did so far, but I'm not sure it's right:

$f_X(x|X<1/2)=2$, which is also uniform, so the expected value is just $\frac{a+b}2=\frac{0+\frac12}2=\frac14$

Answer 1

Yes (but you should not write that the conditional density is $2$, you should write that it is $2$ for $0 < x < 1/2$ and $0$ otherwise).