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# More on Random Variables

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Expectation  ::  Properties  ::  Pairs  ::  Independence  ::  Two R.V.S.  ::  Functions  ::  Inequalities  ::  Conditional  ::  General

## Properties of Expectations

1. If then .
2. If then .

acts kind of like an integral of over , weighted by . One way that the expectation is expressed is

An integral in this form is said to be a Lebesgue-Stieltjes Integral. Since induces a probability on , as we have observed we can also think of the probability space . We can write

where now is the ''identity'' r.v. on the real line. We thus have two equivalent definitions:

Back to properties:

1. If then

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 31). More on Random Variables. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lec2_2.html. This work is licensed under a Creative Commons License