Poisson Distribution

Definition

It is a discrete probability distribution named after French Mathematician Simeon Denis Poisson which expresses the probability of a given number of events that occur in affixed time interval given that the events are independent and occur at a given constant rate. The formula for the distribution is;

poisson distribution formula

Poisson Distribution Derivation

The formula is usually derived from the binomial distribution by substituting p and letting n increase without bound. This is because in a binomial distribution the mean (µ) is given by n*p.

Recall that the pmf of binomial distribution

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