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.
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© 1997 Springer Science+Business Media New York
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Fristedt, B., Gray, L. (1997). Conditional Expectations. In: A Modern Approach to Probability Theory. Probability and its Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-2837-5_23
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DOI: https://doi.org/10.1007/978-1-4899-2837-5_23
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4899-2839-9
Online ISBN: 978-1-4899-2837-5
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