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

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

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

**Cumulative distribution function** of geometrical distribution is

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

**Variance** is

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.

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