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2014 | OriginalPaper | Chapter
8. Conditional Expectations
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Abstract
If there is partial information on the outcome of a random experiment, the probabilities for the possible events may change. The concept of conditional probabilities and conditional expectations formalizes the corresponding calculus.
We start by defining conditional probabilities given events and then generalize to conditional probabilities and expectations given (the information of) aσ-algebra. Finally, we consider the concept of the regular version of the distribution of a random variable given aσ-algebra.