LEC11 Poisson

LEC11 Poisson - Poisson Distribution r.v X = number of...

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Poisson Distribution r.v. X = number of events in an interval Probability Distribution Function: f x P X x e x x ( ) ( ) ! = = = λ 0,1, ... Parameter: λ = E(no. of events in interval) Mean and Variance: E X V X ( ) ( ) = = λ λ

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Examples r.v. X = number of defects (not defectives) on a 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 r.v. X = number of trucks that arrive to a loading dock in an hour 0 1.0 hrs 2
3 Properties of the Poisson Distribution 1. Events proportional to interval size If E(# trucks in an hour) = 3.2 then E(# trucks in two hours) = 6.4 2. Homogeneous intervals E(# trucks between 2:00 and 3:00) = E(# trucks between 4:00 and 5:00) 3. Independent intervals P(0 trucks from 2:00 - 3:00 / 10 trucks from 1:30 - 2:00) = P(0 trucks from 2:00 - 3:00) 3

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Insurance Claims On average, 3.2 customers file a major claim to an insurance company per year. Find the probability that 3 or more customers file a claim in a year. r.v. X = number of major claims filed in a year r.v. X Poisson (

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