applied probability and stochastic processes - bryc

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1、AppliedProbabilityandStochasticProcessesLectureNotesfor577/578ClassWlodzimierzBrycDepartmentofMathematicsUniversityofCincinnatiP.O.Box210025Cincinnati,OH45221-0025E-mail:bryc@ucbeh.san.uc.eduCreated:October22,1995Printed:March21,1996c1995WlodzimierzBry

2、cnnecaiTCiFesrxitetnContentsIProbability31Randomphenomena11.1Mathematicalmodels,andstochasticmodels:::::::::::::::::11.2Eventsandtheirchances::::::::::::::::::::::::::::21.2.1UniformProbability::::::::::::::::::::::::::31.2.2GeometricProbability:::::::

3、::::::::::::::::::51.3Elementaryprobabilitymodels:::::::::::::::::::::::::51.3.1Consequencesofaxioms::::::::::::::::::::::::51.3.2Generaldiscretesamplespace:::::::::::::::::::::61.3.3Generalcontinuoussamplespace:::::::::::::::::::61.4Simulatingdiscrete

4、events:::::::::::::::::::::::::::71.4.1Genericsimulationtemplate::::::::::::::::::::::81.4.2Blindsearch:::::::::::::::::::::::::::::::91.4.3Application:Travelingsalesmanproblem:::::::::::::::101.4.4Improvingblindsearch:::::::::::::::::::::::::121.4.5Ra

5、ndompermutations:::::::::::::::::::::::::131.5Conditionalprobability:::::::::::::::::::::::::::::141.5.1Propertiesofconditionalprobability:::::::::::::::::141.5.2Sequentialexperiments:::::::::::::::::::::::::151.6Independentevents::::::::::::::::::::::

6、:::::::::161.6.1Randomvariables::::::::::::::::::::::::::::171.6.2Binomialtrials:::::::::::::::::::::::::::::171.7Furthernotesaboutsimulations::::::::::::::::::::::::191.8Questions::::::::::::::::::::::::::::::::::::192Randomvariables(continued)212.1Di

7、screter.v.::::::::::::::::::::::::::::::::::212.1.1Examplesofdiscreter.v.:::::::::::::::::::::::222.1.2Simulationsofdiscreter.v.::::::::::::::::::::::222.2Continuousr.v.:::::::::::::::::::::::::::::::::232.2.1Examplesofcontinuousr.v.:::::::::::::::::::

8、:::232.2.2Histograms:::::::::::::::::::::::::::::::242.2.3Simulationsofcontinuousr.v.:::::::::::::::::::::242.3Expectedvalues:::::::::::::::::::::::::::::::::252.3.1Tailintegrationformulas::::::::::::::::::::::::262.3.2Chebyshev-Markovi