Negative Binomial Distribution

En læringskomponent til beregning af sandsynligheder for en negativ binomialfordeling.

Indstillinger

countTrials | boolean: sættes til sand, hvis der i stedet for at tælle antallet af fejl indtil r-te succes skal defineres en tilfældig variabel fra en negativ binomialfordeling som antallet af forsøg indtil r-te succes. Default: false.
step | (number|string): trinstørrelse for rulleindgangen. Default: 0.01.
style | object: CSS inline-stilarter. Default: {}.

Live Editor

<LearnNegativeBinomialDistribution />

<LearnNegativeBinomialDistribution />

Resultat

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