Question

What is expectation and conditional mean, variance?

Answer 1

The conditional mean is described as the expected value of a random variable that is computed by taking on average over large number of occurance.

The conditional variance is described as the variance of a random variable that is given the value of one or more variables. It is calculated like a variance. The conditional variance of X on Y is defined by:

$Var(X|Y)=E[(X-E[X|Y])^2|Y]$