I'm a little bit confused with the deterministic of sample average, so I have sample X and Y, where X is composed of $x_1,x_2,...x_n$, $\bar{X}$ is the sample average. Can I say: $E[\frac{Y}{\bar{X}}|X] = \frac{E[Y|X] }{\bar{X}}$? I think so because if I condition on the whole X, it means I know the whole sample, so for sure I know the sample average, so X bar becomes deterministic under such conditional expectation, thus I could take it out of the expectation, am I coorect?
Thank you a lot