Law of Iterated Expectations

Posted: May 5, 2014 in Educational Material
Tags: , , , ,

The Law of Iterated Expectations (or the Tower Property),  is a very useful -and very intuitive- result:Tower property image

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Or, “the smaller information set always prevails”. Of course the conditioning sets can be anything, but viewing them as information sets increases intuition. I recently wrote a good answer  in Cross Validated on the matter, that contains both an informal intuitive approach and a formal one that has the benefit of being short, and showing that indeed, the Tower Property derives directly from the definition of the conditional expectation. In addition, the thread also contains another answer that shows the rather more tedious derivation using probability mass functions.

The link :

http://stats.stackexchange.com/questions/95947/a-generalization-of-the-law-of-iterated-expectations/95972#95972

 

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