How to Compute the Moments of the Poisson Distribution - dummies

How to Compute the Moments of the Poisson Distribution

By Alan Anderson

As with the binomial and geometric distributions, you can use simple formulas to compute the moments — expected value, variance, and standard deviation — of the Poisson distribution.

How to calculate the expected value of the Poisson distribution

You can find the expected value of the Poisson distribution by using the formula,

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For example, say that on average three new companies are listed in the New York Stock Exchange (NYSE) each year. The number of new companies listed during a given year is independent of all other years. The number of new listings per year, therefore, follows the Poisson distribution, with a value of

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As a result, the expected number of new listings next year is

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How to compute the variance and standard deviation of the Poisson distribution

You can compute the variance and the Poisson distribution as

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So, in the NYSE listing example, the variance equals 3 and the standard deviation equals

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