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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? The parameter is ° = ° T = (1.7 calls/ 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. •. These two properties basically

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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 arrival in each small interval is the same for each interval (i.e. an arrival is equally likely at any time).
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15 Poisson 2 - The Poisson Process The most useful...

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