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21 The Exponential Distribution - Queen's U

21 The Exponential DistributionFrom Discrete- time to continuous - time :In Chapter 6 of the text we will be considering markov processes in con-tinuous time . In a sense, we already have a very good understanding ofcontinuous- time markov chains based on our theory for discrete-timeMarkov chains. For example, one way to describe a continuous -timeMarkov chain is to say that it is a discrete- time markov chain , exceptthat we explicitly model the times between transitions with contin-uous, positive-valued random variables and we explicity consider theprocess at any timet, not just at transition single most important continuous Distribution for building andunderstanding continuous - time markov chains is the Exponential dis- tribution , for reasons which we shall explore in this THE Exponential DISTRIBUTIONThe Exponential Distribution .

understanding continuous-time Markov chains is the exponential dis-tribution, for reasons which we shall explore in this lecture. 177. 178 21. THE EXPONENTIAL DISTRIBUTION The Exponential Distribution: A continuous random variable X is said to have an Exponential(λ)

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