# Worksheet for how to calculate Negative Binomial Distribution

The Negative Binomial is discrete probability distribution of number of failures that occurs at the beginning of the sequence until the given number of successes to be achieved and is a statistical experiment has the following properties:
Properties:
1. The experiment consists of x repeated trials
2. Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other is a failure
3. The probability of success, denoted by P, is the same on every trial
4. The trials are independent (i.e) the outcome of one trial does not affect the outcome of other trials
5. The experiment continues until r successes are observed, where r is specified in advance

Formula:

Negative Binomial Distribution = n-1Cr-1 x Pr x (1 - P)n - r

Example:
Calculate the Negative Binomial Distribution for the values of N = 5, R = 3 & P = 0.2
Substitute these values in the above formula,
Negative Binomial Distribution = 5-1C3-1 x (0.2)3 x (1 - 0.2)5 - 3
= (4x3/2x1) x 0.008 x 0.262144
= 0.0307

When you try such calculations on your own, this negative binomial distribution calculator can be used to verify your results of calculations.