Abstract
Let X and Y be two random variables with Y taking values in R with X taking on only countably many values. It often arises that we know already the value of X and want to calculate the expected value of Y taking into account the knowledge of X. That is, suppose we know that the event {X = j| for some value j has occurred. The expectation of Y may change given this knowledge. Indeed, if Q(∧) = P∧|X = j), it makes more sense to calculate E Q {Y{ than it does to calculate Ep{Y| (E R {·| denotes expectation with respect to the Probability measure R.)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Jacod, J., Protter, P. (2004). Conditional Expectation. In: Probability Essentials. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55682-1_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-55682-1_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43871-7
Online ISBN: 978-3-642-55682-1
eBook Packages: Springer Book Archive