post17 - STAT 511-2 Spring 2012 Lecture 17 Feb 20, 2012 Jun...

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1 STAT 511-2 Spring 2012 Lecture 17 Feb 20, 2012 Jun Xie 4.4 The exponential distribution The exponential distribution is frequently used as a model for the distribution of times between the occurrence of successive events, such as customers arriving at a service facility or calls coming in to a switchboard. Proposition Suppose that the number of events occurring in any time interval of length t has a Poisson distribution with parameter t (where , the rate of the event process, is the expected number of events occurring in 1 unit of time) and that numbers of occurrences in nonoverlapping intervals are independent of one another. Then the distribution of elapsed time between the occurrence of two successive events is exponential with parameter = . Although a complete proof is beyond the scope of the text, the result is easily verified for the time X 1 until the first event occurs: P ( X 1 t ) = 1 – P ( X 1 > t ) = 1 – P [no events in (0, t )] which is exactly the cdf of the exponential distribution. Another important application of the exponential distribution is to model the distribution of component
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post17 - STAT 511-2 Spring 2012 Lecture 17 Feb 20, 2012 Jun...

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