Negative Binomial Distribution

A learning component for calculating probabilities of a negative binomial distribution.

Options

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

Live Editor

<LearnNegativeBinomialDistribution />

<LearnNegativeBinomialDistribution />

Result

For number of successes until experiment is stopped r = and a success probability of p = we get

P (X = x) = (\binom{x + 10 - 1}{x}) {0.5}^{10} {0.5}^{x}

Evaluated at x = we get

P (X = 0) = (\binom{9}{0}) {0.5}^{10} {0.5}^{0} \approx 0.0010

The random variable X denotes the number of failures until the r-th success is reached.

Successes until stop (r):

Success probability (p):

x0:
029

P (X \leq 0) = 0.001

Successes until stop (r):

Success probability (p):

x0:
029

P (X > 0) = 0.999

Successes until stop (r):

Success probability (p):

x0:
029

x1:
029

P (0 \leq X \leq 1) = 0.0059