Poisson_examples

# Poisson_examples - Poisson Distribution This is a distribution useful for modeling of the number of events occuring in an interval of space or time

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Poisson Distribution This is a distribution useful for modeling of the number of events occuring in an interval of space or time, for example, the number of automobiles arriving at a toll booth during a 10-minute period or the number of weak points in a square meter of plastic sheeting. The expected number of events that occur in one period or region is constant and is called the rate parameter and is usually denoted by λ . The requirements for a Poisson distribution are that (a) no two events can occur simultaneously , (b) events occur independently in diFerent intervals, and (c) that the expected number of events in each time interval remain constant. The probability mass function of a Poisson random variable X is given by p ( x ) = e - λ λ x x ! , x = 0 , 1 , 2 , . . . where p ( x ) = P ( X = x ), that is the probability that there are exactly x occurrences of an event in a speci±ed interval, given that the expected number of occurrences of the event in the interval is λ . ²or
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## This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.

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