Search Back to top Filter ResultsLocationBookshelves (1)ClassificationArticle typeBook or UnitChapterSection or PageN/AN/AAuthorDavid LaneAlexander AueJohn H. McDonaldOpenStaxOpenIntro StatisticsDebashis PaulLarry GreenDiane KiernanAlexey ShipunovPeter KaslikKathryn KozakDavid LiljaKristin KuterFoster et al.Jenkins-Smith et al.Grinstead & SnellRussell A. PoldrackThomas K. TiemannDanielle NavarroJonathan A. PoritzKyle SiegristPaul PfeifferMatthew J. C. CrumpMichelle OjaRachel WebbAlex ReinhartMaurice A. GeraghtyAnonymousErich C Fein, John Gilmour, Tayna Machin, and Liam HendryGordon E. SartyPenn State's Department of StatisticsMark GreenwoodYang Lydia YangBill PelzValerie WattsNancy IkedaLinda R. Cote, Rupa G. Gordon, Chrislyn E. Randell, Judy Schmitt, and Helena MarvinKlaire SomorayHannah Seidler-WrightMichael R DohmChristina R. PeterLumen LearningRoger ClarkMikaila Mariel Lemonik ArthurMikaila Mariel Lemonik Arthur and Roger ClarkYvonne AnthonyJaeyong ChoiCover PageyesTOC OnlyCompile but don't publishLicensePublic DomainCC BYCC BY-SACC BY-NC-SACC BY-NDCC BY-NC-NDGNU GPLAll Rights ReservedCC BY-NCGNU FDLShow TOCyesnoEmbed JupyterpythonoctaversagemathTranscludedyesOER program or PublisherCollege of the Canyons - Zero Textbook Cost ProgramASCCC OERI ProgramCK-12OpenStaxGALILEOOpenSUNYMIT OpenCourseWareVirginia Tech Libraries' Open Education InitiativeThe Publisher Who Must Not Be NamedeCampusOntarioWAC ClearinghouseBC CampusLumenOpen OregonOpenStax CNXPDXOpenEvergreen Valley CollegeAutonumber Section Headingstitle with space delimiterstitle with colon delimiterstitle with dash delimitersLicense Version1.01.32.02.53.04.0Include attachmentsContent TypeDocumentImageOther Searching inAll resultsAbout 1 results4.7: Conditional Expected Valuehttps://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/04%3A_Expected_Value/4.07%3A_Conditional_Expected_Value\begin{align} \cov(Y, Z \mid X) & = \E\left(Y Z - Y \E(Z \mid X) - Z E(Y \mid X) + \E(Y \mid X) E(Z \mid X) \biggm| X \right) = \E(Y Z \mid X) - \E\left[Y \E(Z \mid X) \mid X\right] - \E\left[Z \E(Y \...\begin{align} \cov(Y, Z \mid X) & = \E\left(Y Z - Y \E(Z \mid X) - Z E(Y \mid X) + \E(Y \mid X) E(Z \mid X) \biggm| X \right) = \E(Y Z \mid X) - \E\left[Y \E(Z \mid X) \mid X\right] - \E\left[Z \E(Y \mid X) \mid X\right] + \E\left[\E(Y \mid X) \E(Z \mid X) \mid X\right] \\ & = \E\left(Y Z \mid X\right) - \E(Y \mid X) \E(Z \mid X) - \E(Y \mid X) \E(Z \mid X) + \E(Y \mid X) \E(Z \mid X) = \E\left(Y Z \mid X\right) - \E(Y \mid X) E(Z \mid X) \end{align}MoreShow more results
