# Geometric Distribution. Probability density function, cumulative distribution function, mean and variance

This calculator calculates geometric distribution pdf, cdf, mean and variance for given parameters

### This page exists due to the efforts of the following people:

#### Timur

Created: 2018-01-26 07:26:07, Last updated: 2021-02-13 11:04:37

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/7693/. Also, please do not modify any references to the original work (if any) contained in this content.

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure," in which the probability of success is the same every time the experiment is conducted. wikipedia

When we want to know the probability of k successes in n such trials, we should look for the probability of k-th point in probability density function of the binomial distribution, for example here - Binomial distribution, probability density function, cumulative distribution function, mean and variance.
But if we want to know the probability of getting the first "success" on k-th trial, we should look into geometric distribution

Probability density function of geometrical distribution is
$f(x)=(1-p)^{x-1}p$
Cumulative distribution function of geometrical distribution is
$F(x)=1-(1-p)^{x}$
where p is probability of success of a single trial, x is the trial number on which the first success occurs.

Note that f(1)=p, that is, the chance to get the first success on the first trial is exactly p, which is quite obvious.

Mean or expected value for the geometric distribution is
$\mu_x=\frac{1}{p}$

Variance is
$\sigma^{2}_{x}=\frac{1-p}{p^2}$

The calculator below calculates the mean and variance of geometric distribution and plots the probability density function and cumulative distribution function for given parameters: the probability of success p and the number of trials n.

#### Geometric Distribution. Probability density function, cumulative distribution function, mean and variance

Digits after the decimal point: 2
Mean

Variance

Geometric distribution
The file is very large. Browser slowdown may occur during loading and creation.
Cumulative distribution function
The file is very large. Browser slowdown may occur during loading and creation.

URL copied to clipboard
PLANETCALC, Geometric Distribution. Probability density function, cumulative distribution function, mean and variance