BINOMIAL AND GAUSSIAN
Analysis of the relationship between the two random variables
![]()
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.
![]()
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().
![]()
![]()
Copyright © 1998 Rensselaer Polytechnic Institute. All Rights Reserved.