Here, we will discuss the properties of conditional expectation in more detail as they are quite useful in practice. We will also discuss conditional variance.

The conditional variance tells us how much variance is left if we use to "predict" Y. Here, as usual, stands for the conditional expectation of Y given X, which we may recall, is a random variable …

LECTURE 13: Conditional expectation and variance revisited; Application: Sum of a random number of independent r.v.'s A more abstract version of the conditional expectation view it as …

We can also find the expectation and variance of X with respect to this condi-tional distribution. That is, if we know that the value of Y is fixed at y, then we can find the mean value of X given …

Jul 8, 2025 · Expected Conditional Variance: This measures how much the variable Y varies on average when we know the value of another variable X. Variance of the Conditional …

A. Properties of conditional expectation that one random variable. Let X; Y; Z be iscrete random variables. Then E[Xj = y; Z = z] makes sense. We can think of it as a functio of the random out …

There are a lot of “rules” for manipulating conditional expectations, and the hope of this document is to get you comfortable with all the main ones. Here we list the rules, and in the next section …

That’s all there is to Conditional Probability, Condition Expectation and Condition Variance. You can see how useful and central a role these three concepts play in regression modeling.

We'll start by giving formal definitions of the conditional mean and conditional variance when X and Y are discrete random variables. And then we'll end by actually calculating a few!

Conditional expectation has all the usual properties of expectation since it is essentially the expectation you would compute for the reduced sample space f 2 : X( ) xg;