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An Exploration of Random Processes for Engineers(by Bruce Hajek)

An Exploration of Random Processes for Engineers(by Bruce Hajek)

ID：39775214

大小：2.96 MB

页数：381页

时间：2019-07-11

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1、NotesforECE534AnExplorationofRandomProcessesforEngineersBruceHajekJanuary5,2009c2008byBruceHajekAllrightsreserved.Permissionisherebygiventofreelyprintandcirculatecopiesofthesenotessolongasthenotesareleftintactandnotreproducedforcommercialpurposes.Emailtob-hajek@illinois.edu,pointingoute

2、rrorsorhardtounderstandpassagesorprovidingcomments,iswelcome.Contents1GettingStarted11.1Theaxiomsofprobabilitytheory.............................11.2Independenceandconditionalprobability........................51.3Randomvariablesandtheirdistribution.........................81.4Functions

3、ofarandomvariable..............................111.5Expectationofarandomvariable.............................161.6Frequentlyuseddistributions...............................201.7Jointlydistributedrandomvariables...........................231.8Crossmomentsofrandomvariables................

4、............241.9Conditionaldensities....................................261.10Transformationofrandomvectors............................261.11Problems..........................................292ConvergenceofaSequenceofRandomVariables372.1Fourde nitionsofconvergenceofrandomvariables....

5、...............372.2Cauchycriteriaforconvergenceofrandomvariables..................472.3Limittheoremsforsequencesofindependentrandomvariables............512.4ConvexfunctionsandJensen'sinequality........................542.5Cherno boundandlargedeviationstheory.......................552.6

6、Problems..........................................583RandomVectorsandMinimumMeanSquaredErrorEstimation673.1Basicde nitionsandproperties..............................673.2Theorthogonalityprincipleforminimummeansquareerrorestimation........693.3Conditionalexpectationandlinearestimators...

7、...................723.3.1Conditionalexpectationasaprojection.....................733.3.2Linearestimators..................................743.3.3Discussionoftheestimators............................753.4JointGaussiandistributionandGaussianrandomvectors...............773.5Linea

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