Let's say that the conditional PDF of random variables $\Omega$ and $Z$ is $$f_{\Omega\mid Z}(\omega\mid z)= \begin{cases} k\omega z, & 0 < \omega,z < 1, \\ 0,& \text{otherwise.}\end{cases}$$
For the PDF to be normalized, $k=4$.
Is the conditional expectation estimator of $Ω$ based on the observed value of $Z$ simply just $\int_0^1 w(4wz) \, dw=\frac{4z}{3}$? I want to know if my understanding on conditional expectation estimator is correct.