Lec11 Poisson Distribution

# Lec11 Poisson Distribution - Insurance Claims 5 8 or more...

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Poisson Distribution 1

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Poisson Distribution: Examples 2 r.v. X = number of events in an interval Possible values X=0, 1, 2, … r.v. X = number of defects on a square inch of painted surface r.v. X = number of earthquakes in a year r.v. X = number of typographical errors on a page r.v. X = number of customers that arrive in an hour
Poisson pdf 3

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What assumptions lead to this? Totally random! 4 r.v. X = arrivals to NY Penn station per hour (during peak hours) 1. Proportional – if expected arrivals in 1 hour is 5, then expected arrivals in 2 hours is 10 2. Homogeneous – expected arrivals per hour is same, no matter which hour you pick 3. Independent – arrivals from 12:00 to 12:05 is independent of number for any other interval

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Unformatted text preview: Insurance Claims 5 8 or more in a year means bankruptcy More…insurance 6 Ex: arrivals to the Emergency Room 7 The number of arrivals to an emergency room overnight has the Poisson distribution with mean 8.2 per hour. Find the probability of 0 arrivals in an hour. Find the probability of 0 arrivals in an hour given there were 40 arrivals in the preceding hour. (Hint: I flipped a coin and got 10 heads in a row – find the probability the next flip is a heads.) Ex: Particulates on a Silicon Wafer 8 The number of defects on a cable has Poisson distribution with mean 0.47 per foot. Find the probability of no defects in 2 inches....
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Lec11 Poisson Distribution - Insurance Claims 5 8 or more...

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