Poisson

# Poisson - Poisson Distribution The Poisson Distribution is...

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Poisson Distribution The Poisson Distribution is used to model the number of rare events that occur in space, time, volume, or any other dimension. For this distribution, The average number of events in a given time period or space is λ . The number of events in non-overlapping time periods or spaces are independent. The probability of one event in a short time period or space h is λh . The probability of more than one event in a short time period or space h is 0. The random variable Y = number of events in a given time period or space. The parameter for the Poisson random variable Y is λ . The probability distribution function for the Poisson random variable Y is P ( Y = y ) = p ( y ) = λ y e - λ y ! y = 0 , 1 , 2 , . . . The theoretical mean of the Poisson random variable Y is E ( Y ) = λ The variance of the Poisson random variable Y is V ( Y ) = λ A Poisson distribution can be used to model the number of accidents that occur within a week at a

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