# What is the variance of a geometric distribution for a given pobability?

Nov 15, 2015

variance $= \frac{1 - p}{p} ^ 2$

#### Explanation:

For example, a geometric with p=0.4 ...

mean $= \frac{1}{p} = \frac{1}{0.4} = 2.5$

variance $= \frac{1 - p}{p} ^ 2 = \frac{1 - 0.4}{0.4} ^ 2 = \frac{0.6}{0.16} = 3.75$

s.d. $= \sqrt{3.75} \approx 1.9365$

hope that helped