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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

Timur

Created: 7 years ago, Last updated: 4 years ago

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.

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

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

Digits after the decimal point: 2
Mean
2
Variance
2
Geometric distribution
The file is very large. Browser slowdown may occur during loading and creation.
123456789100.000.050.100.150.200.250.300.350.400.450.50

Geometric distribution

Trial numberProbability of the first success
10.5
20.25
30.125
40.0625
50.0313
60.0156
70.0078
80.0039
90.0020
100.0010
Items per page:
1 - 10 of 10
Cumulative distribution function
The file is very large. Browser slowdown may occur during loading and creation.
123456789100.500.550.600.650.700.750.800.850.900.951.00

Cumulative distribution function

Trial numberDistribution function
10.5
20.75
30.875
40.9375
50.9688
60.9844
70.9922
80.9961
90.9980
100.9990
Items per page:
1 - 10 of 10

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PLANETCALC, Geometric Distribution. Probability density function, cumulative distribution function, mean and variance
Timur4 years ago

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