November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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5.2 EXPECTATION AND INTEGRATION
Consider first the abstract probability space 
, and let X be a random variable that maps outcomes in Ω to 
.
Definition: Expectation The expectation of random variable X is
which is the Lebesgue integral of function 
and P is the probability measure for the event space 
.
The Lebesgue integral is briefly described in Appendix D. All outcomes that map from Ω to 
are weighted by the probability measure P above to give the expectation. We can also write 
entirely in terms of the random variable with probability space 
as follows:
where FX(x) is the cumulative ...
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