Transcription of Topic 7: Random Processes - Tufts University
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Topic 7: Random Processes - Tufts University
Topic7: RandomProcesses De nition,discreteandcontinuousprocesses Specifyingrandomprocesses{Joint cdf's or pdf's{Mean,auto-covariance,auto-correlat ion{Cross-covariance,cross-correlation StationaryprocessesandergodicityES150{ Harvard SEAS1 Randomprocesses Arandomprocess, alsocalledastochasticprocess, is a familyof randomvariables,indexedby a parametertfromanindexingsetT. For eachexperiment outcome!2 ,we assigna functionXthatdependsontX(t; !)t2T; !2 {tis typicallytime,butcanalsobe a spatialdimension{tcanbe discreteor continuous{Therangeoftcanbe nite,butmoreoftenis in nite,which meanstheprocesscontainsanin nitenumber of randomvariables.}}}}}}}
Topic 7: Random Processes † Deflnition, discrete and continuous processes ... In many random processes, the statistics do not change with time. The behavior is time-invariant, even though the process is random. ... Xn = §1 with probability 1 2 for n even Xn = ¡1=3 and 3 with probabilities 9 10 and 1 10 for n odd
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