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Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Iterated expectation

Somebody teach me iterated expectations please?

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Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Iterated expectation

From what I understand on Wikipedia, it’s the expectation of an expectation, the second expectation being treated like a random variable. For example, if X and Y are random variables and y is in the sample space of Y, we define the conditional expectation

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(where P(X = x | Y = y) denotes that probability that X = x given that Y = y). This is a function of y and so can be regarded as a random variable: Z = E(X|Y). The expectation of Z, E(Z), is then an iterated expectation:

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So an iterated expectation is just the expectation of an expectation. In fact, the theorem on Wikipedia states that E(Z) = E(X) for this particular iterated expectation.

Last edited by Olinguito (2014-08-14 12:06:46)

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