Poisson Process Expected Arrival Time

Problem

For a Poisson process with rate lam, the time of the k-th event is the sum of k independent exponential interarrival times, each with mean 1 / lam. Return the expected time of the k-th event, which is k / lam. Return 0.0 for lam <= 0 or k < 0, and 0.0 for k = 0.

Hint

Linearity of expectation over the k independent interarrival times.

Test cases

case 1

in: [2,3]

expected: 1.5

case 2

in: [0.5,1]

expected: 2

case 3

in: [1,0]

expected: 0

case 4

in: [4,2]

expected: 0.5

case 5

in: [0.25,5]

expected: 20

Starter codePython

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

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