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,
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
As a result, the expected number of new listings next year is
How to compute the variance and standard deviation of the Poisson distribution
You can compute the variance and the Poisson distribution as
So, in the NYSE listing example, the variance equals 3 and the standard deviation equals
