Negative Hypergeometric PMF

Problem

Negative hypergeometric probability that the r-th success in sampling without replacement occurs on draw k.

P(X = k) = C(k - 1, r - 1) * C(pop - k, successes - r) / C(pop, successes). Return 0.0 for invalid combinations of arguments.

Hint

Place r - 1 successes in the first k - 1 draws and make draw k a success.

case 1

in: [10,3,5,2]

expected: 0.16666666666666666

case 2

in: [5,2,2,2]

expected: 0.1

case 3

in: [10,3,1,1]

expected: 0.3

case 4

in: [4,2,3,2]

expected: 0.3333333333333333

case 5

in: [10,3,12,1]

expected: 0

Starter codePython

import math


def negative_hypergeometric_pmf(pop, successes, k, r):
    # Your code here
    pass

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