[Mathematics | Probability | Statistics | Distribution] The variance of a set of numbers is the measure of how spread out they are. A variance of zero indicates that there is no variance which means all of the values are the same. Variance can never be represented with a negative number. The higher the variance the more spread out the values in the data set are.

The Pascal distribution (after Blaise Pascal) is a special cases of the negative binomial. A Pascal experiment calculates the number of Bernoulli trials needed to get `r` amount of successes.

The inputs to this equation are the probability of success, p, of for mutually independent Bernoulli trials and the number of failures that are probable before success occurs, r.

Variables:

• `p` = Success Rate
• `r` = Successes wanted
• Equations:
• `(r * (1-p))/p^2`

Notes

A Pascal random variable X has the probability mass function:

`f(x) = ((n-1+x),(x)) *p^n*(1-p)^x`, for x = 0,1, 2...

The Pascal Distribution, also known as the negative binomial distribution, can be used to model the number of failures that will likely happen before you achieve success.  This is for mutually independent Bernoulli trials wher the success probability is defined as p.