Lots of answers online on what is $E[X|Y]$ if $X$ is independent of $Y$ (that would imply $E[X|Y] = E[X]$).
However, what if the correlation of $X$ and $Y$ is not zero? To work with actual values, what is $E[X|Y]$ if:
- $X$ is normally distributed as $N(\mu_X=2,\sigma_X^2=3)$
- $Y$ is normally distributed as $N(\mu_X=0,\sigma_Y^2=1)$
- $corr(X,Y)=\rho$ (some number between $-1$ and $1$, but not necessarily $0$)