Transcription of Chapter 9 Poisson processes - Yale University
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Page 1 Chapter 9 Poisson processesThe Binomial distribution and the geometric distribution describe the behavior of tworandom variables derived from the random mechanism that I have called coin tossing . Thenamecoin tossingdescribes the whole mechanism; the namesBinomialandgeometricreferto particular aspects of that mechanism. If we increase the tossing rate to m tosses per sec-ond and decrease the probability of heads to a small p, while keeping the expected numberof heads per second fixed at Dmp, the number of heads in atsecond interval will haveapproximately a ;p/distribution, which is close to the Poisson .
A Poisson process with rate‚on[0;1/is a random mechanism that gener- ates “points” strung out along [0 ; 1 / in such a way that (i) the number of points landing in any subinterval of lengtht is a random variable with
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