MediumProbabilitypr-073

Poisson Process Probability

Problem

Probability that a Poisson process with rate lam has exactly k events in the time interval (t1, t2).

The count is Poisson distributed with mean lam * (t2 - t1). Return 0.0 when lam < 0, t2 < t1 or k < 0.

Hint

Only the interval length enters the mean, not the absolute times.

case 1

in: [2,0,1,0]

expected: 0.1353352832366127

case 2

in: [3,1,3,2]

expected: 0.044617539179994455

case 3

in: [1,0,2,3]

expected: 0.1804470443154836

case 4

in: [1,2,1,1]

expected: 0

Starter codePython

import math


def poisson_process_probability(lam, t1, t2, k):
    # Your code here
    pass

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