Geometric Distribution

A learning component for calculating probabilities of a geometric distribution.

Options

countTrials | boolean: set to true if instead of counting the number of failures until the first success, a random variable from a geometric distribution should be defined as the number of trials until the first success. Default: false.
step | (number|string): step size of the scroll input. Default: 0.01.
style | object: CSS inline styles. Default: {}.

Live Editor

<LearnGeometricDistribution />

<LearnGeometricDistribution />

Result

Let $X$ be the number of failures until the first success.

For success probability of p = we get

P (X = x) = {(1 - 0.5)}^{x - 1} 0.5

Evaluated at x = we get

P (X = 0) = {(1 - 0.5)}^{0} 0.5 = 0.5000

Success probability:
0.011

x0:
-110

P (X \leq 0) = 0.5

Success probability:
0.011

x0:
-110

P (X > 0) = 0.5

Success probability:
0.011

x0:
-110

x1:
-110

P (0 \leq X \leq 1) = 0.75