This is a simple consequence of the measure-theoretic definition of conditional expectation. By definition, is a -measurable random variable that satisfies for every measurable set .

Apr 18, 2016 · In the second expectation, you're finding the expected value $Y$, given that you have $X$. One way to think of it is you first integrate with respect to $y$, holding $X=x$ constant, i.e. you …

Double Expectation: E(Y ) = E[E(Y jX)] Theorem A on page 149 To make sense of this, note While E(Y jX = x) = R y fjX(yjx) dy

Feb 26, 2024 · 2,-2 \/é) Find E (X) by using the “double expectation formula” E (X) = E| E [X|Y]]. You should E [X|Y] from the table above to take a weighted averagio/fthe two values of E [X|Y] by p (y).

It is essential to memorize this formula for the exam. A tip to help you remember this formula is "EVVE", which stands for "Expected value of Variance, plus Variance of Expected value".

Here's an example of when you would use the double expectation formula.

Mar 16, 2013 · If you've been given the moments (Expectation) of a particular distribution (Courses) that is partitioned according to a separate distribution (Student Proportion), Then you can use Double …

Believe it or not, sometimes it’s easier to calculate E[Y ] indirectly by using our double expectation trick. Example: An alternative way to calculate the mean of the Geom(p).

You can, but that requires a different, more general definition of the conditional expectation E[Y ∣ X] E [Y ∣ X] (one not using densities, of course). Are you familiar with such?

Jan 10, 2018 · Double expectations example involving 3 doors. E (X) solved directly from definition - leads to a geometric distribution.