Poisson Process Count Probability

Problem

For a Poisson process with rate lambda, the number of events in time t is Poisson(lambda t), so P(N(t) = k) = exp(-lambda t)(lambda t)^k / k!.

Given lambda, t, and k, return the probability.

Hint

The rate integrates to lambda t over the interval.

case 1

in: [2,1,3]

expected: 0.1804470443154836

case 2

in: [0.5,4,0]

expected: 0.1353352832366127

case 3

in: [1,2,2]

expected: 0.2706705664732254

Starter codePython

def poisson_process_count_probability(lam, t, k):
    # Your code here
    pass

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