Superposition of Poisson Processes

Problem

Two independent Poisson processes with rates lam1 and lam2 are merged. Return the probability that the superposed process has exactly k events in time t.

The merged process is Poisson with rate lam1 + lam2. Return 0.0 for negative inputs.

Hint

Adding independent Poisson processes adds their rates.

Test cases

case 1

in: [1,2,1,0]

expected: 0.049787068367863944

case 2

in: [1,1,1,2]

expected: 0.2706705664732254

case 3

in: [0,0,5,0]

expected: 1

case 4

in: [2,1,2,3]

expected: 0.08923507835998891

Starter codePython

import math


def superposition_poisson_probability(lam1, lam2, t, k):
    # Your code here
    pass

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