Lecture 12

# The pdf of the exponential distribution with

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Unformatted text preview: 1 ms 1500 2000 3 2 ms 1750 2000 7 4 ms CS 522, v 0.94, d.medhi, W’99 T 13 7. On exponential distribution This is a good time to quickly go over a couple of things about exponential distribution. The pdf of the exponential distribution with parameter  is given by f x = e,x x 0 : The mean and the variance are given by 1 V X  = 2 : 1 E X  =  8. Poisson Process A pure-birth homogeneous process, i.e., j A stochastic process fAtjt with rate  if 1. =0 j = , is a Poisson process. Another way:  0g taking non-negative integer values is said to be a Poisson process fAtg is a counting process. 2. The number of arrival that occur in disjoint time interval are independent. 3. The number of arrivals in interval of length is Poisson distributed with parameter  PrfAt +  , At = ng = exp,  n=n! n = 0 1 ::: Note that exp is the exponential function, expx = ex , where e is the Euler number (=2.718281828...). Important properties of a Poisson process: 1) Interarrival times are independent and exponential...
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## This document was uploaded on 03/19/2014 for the course CS 6030 at Western Michigan.

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