Lecture18[1]

# Lecture18[1] - Lecture 18 Poisson Distribution Section 5.6...

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Poisson Distribution Section 5.6 1 STAT 225, Dallas Bateman, Spring 2010 Lecture 18

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Poisson Distribution Sometimes we are interested in the number of rare events in a large interval. Let be the average number of the rare events in this interval. Such a random variable is called a Poisson random variable with parameter 2 STAT 225, Dallas Bateman, Spring 2010
Poisson Distribution Examples: The number of typos in a magazine. The number of tornados in Indiana. The number of people hit by lightning. 3 STAT 225, Dallas Bateman, Spring 2010

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Poisson Distribution Notation : PMF : Expectation & Variance : Note : If are independent, then λ λ ) ( ) ( X Var X E ! ) ( x e x p x ) ( ~ Pois X ) ( ~ & ) ( ~ 2 2 1 1 Pois X Pois X ) λ Pois(λ ~ X X 2 1 2 1 4 STAT 225, Dallas Bateman, Spring 2010
Poisson Example #1 Earthquakes occur in the western United States with a rate of 2 per week. If we model the number of earthquakes as a Poisson random variable, what is the probability that there will be at least 3 earthquakes in a two-week period?

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Lecture18[1] - Lecture 18 Poisson Distribution Section 5.6...

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