Poisson Distribution

This is a discrete distribution
This distribution is used when events occur at random.
This can be used when large samples are drawn from a population containing a small number of items being considered, the sample size is large and the probability of success is very small

It can be used when the average number of successes are known but the sample size is not known

A possion random variable is a count of the number of events that occur in a certain time interval.
A discrete random variable is said to follow a poisson distribution with parameter m, written
if it probability distribution satisfies the following equation

The following must be met:
1 - the length of the observation period is fixed in advance
2 - the events occur at a constant average rate
3 - the number of events occurring in disjoint intervals are independent

Properties

Assumptions

Excel Functions

POISSON.DIST - The probability of getting less than or equal to a particular value in a poisson distribution.

Poisson(x, mean, cumulative) - gives probability of observing "x" given a mean rate if cumulative is zero.
If cumulative is one it gives probability of 0,1,2,..x
Rounds "x" down to the nearest integer.

Estimating Binomial Distribution

This provides a good approximation to the Binomial Distribution with parameters n and p where the number of observations n is large and the success probability p is small.