Abstract
Integration with respect to conditional distributions gives conditional expectations. A precise definition is given in the first section of this chapter, after which several equivalent formulations are given. An interesting sidelight is the proof, at the end of the first section, of the Radon-Nikodym Theorem. The remaining sections are devoted to various formulas and properties, some of which are analogous to properties obtained in Chapters 4, 5, and 8 for (unconditional) expectations. Conditional variances are also treated and a useful formula relating conditional and unconditional variances is proved.KeywordsConditional DistributionConditional ExpectationConditional VarianceBorel SubsetNull EventThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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