Poisson Distribution

SITUATION
Let the discrete random variable X denote the number of times an event occurs in an interval of time (or space). Then X may be a Poisson random variable with x = 0, 1, 2, ...

EXAMPLES

Let X equal the number of typos on a printed page. (This is an example of an interval of space — the space being the printed page.)
Let X equal the number of cars passing through the intersection of Allen Street and College Avenue in one minute. (This is an example of an interval of time — the time being one minute.)
Let X equal the number of Alaskan salmon caught in a squid driftnet. (This is again an example of an interval of space — the space being the squid driftnet.)
Let X equal the number of customers at an ATM in 10-minute intervals
Let X equal the number of students arriving during office hours

A Poisson distribution is the probability distribution that results from a Poisson experiment.

ATTRIBUTES OF POISSON EXPERIMENT
Explained with following example: Suppose we know the average number of houses sold by XYZ as 2 per day. What is the probability that exactly 3 homes will be sold tomorrow?

The experiment results in either successes or failures

Sell 3 houses or not

The average number of successes (μ) in a given region is known

We know of 2 houses sold per day

The probability that a success will occur is proportional to the size of the region
The probability that a success will occur in an extremely small region is virtually zero.