MediumProbabilitypr-032

Negative Binomial PMF

Problem

Negative binomial probability mass function: probability that the r-th success occurs on trial k.

P(X = k) = C(k - 1, r - 1) * p^r * (1 - p)^(k - r) for k >= r >= 1. Return 0.0 otherwise.

Hint

Arrange r - 1 successes among the first k - 1 trials, then succeed again.

case 1

in: [1,0.5,3]

expected: 0.125

case 2

in: [2,0.5,4]

expected: 0.1875

case 3

in: [3,0.3,5]

expected: 0.07937999999999998

case 4

in: [2,0.5,1]

expected: 0

Starter codePython

import math


def negative_binomial_pmf(r, p, k):
    # Your code here
    pass

4 test cases · run your code against them in the editor