What is the Poisson Distribution?
Example:

An acquisition officer has observed that in a certain manufacturing company of military tools, ten percent of the tools produced turned out to be defective. Now, the acquisition officer was interested in finding out the probability of choosing two defective tools in a sample of ten tools.

This problem can be solved using the concept of the Poisson Distribution. Let us look at the definition of Poisson distribution.


Let X be a discrete random variable which can take on the values 0, 1, 2, .... such that the probability function of X is given by

Poisson Distribution

where '' is a given positive constant. This distribution is called the Poisson distribution and a random variable having this distribution is said to be Poisson distributed.

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Solution:

Now that we know what the Poisson Distribution is , let us solve the problem stated above.

we have

n = 10 ;
p = 0.1 ;
=> = np = (10) (0.1) = 1.

According to the Poisson Distribution we have,

P(X = 2) = [(1)² e^-1] / (2!);

= 0.193

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Properties of Poisson Distribution

Mean
Variance	2
Standard deviation	1/2

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