15 Poisson 2

# 15 Poisson 2 - The Poisson Process The most useful...

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1/5/10 The Poisson Process The most useful application of the Poisson distribution is in the modeling of “purely random processes”, also known as “Poisson processes”. A Poisson Process models an “arrival process”. For example the arrival of emergency patients to a hospital

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1/5/10 Example Calls arrive to a 1-800 number according to a Poisson process with rate & = 1.7 calls per minute. What is the probability that at least 10 calls arrive in the next 10 minutes? min)(10 min) = 17 calls. P(X& 10) = 1 - P(Xr 9) = 1 - 0.026 = 0.99974
1/5/10 The behavior that characterizes a Poisson Process is: 1. On average we see arrivals per time unit 2. An arrival is equally likely to occur at any time.

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1/5/10 Imagine that we divide the time interval [0,T] into a great many equally spaced intervals of width / . There will thus be T/+ such tiny intervals. Next assume that the probability p of 1
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## This note was uploaded on 01/04/2010 for the course STATS 1100 taught by Professor Rodriguez during the Spring '08 term at Pittsburgh.

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15 Poisson 2 - The Poisson Process The most useful...

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