BINOMIAL AND GAUSSIAN

Analysis of the relationship between the two random variables [brown line]


A binomial random variable can be approximated by the Gaussian/Normal random variable. Here is how to do it:

A Binomial random variable X has a mean and variance


where p is the probability of success on each trial.

Probabilities for a binomial random variable X can be approximated by the Gaussian pdf by using a Normal distribution with the same mean and variance as the corresponding Binomial RV.

This estimate works best for large values of n and small values of p.

To get a better estimate, the fact that a Binomial RV is discrete should be acknowledged and the boundaries for integration in the Gaussian should be 1/2 beyond the desired probabilities for the Binomial.

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An example:

For a Binomial random variable with parameters n=10 and p=0.4, to find


You would use


Where

Then



Click Here for a discussion of the ERF().

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RELATED
CONCEPTS

Random Variables
Probability Mass Function
Cumulative Distribution Function
Expectation of a Discrete Random Variable
Important Discrete Random Variables
Gaussian Random Variables
Binomial Random Variables
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