Arcsine Law Last Visit Probability

Problem

Arcsine law for a symmetric simple random walk. Return the probability that the last visit to 0 up to time 2n occurs at time 2k:

P = C(2k, k) * C(2n - 2k, n - k) / 4^n.

Return 0.0 when k lies outside 0..n.

Hint

The last visit splits the walk into two independent excursions.

case 1

in: [1,0]

expected: 0.5

case 2

in: [1,1]

expected: 0.5

case 3

in: [2,0]

expected: 0.375

case 4

in: [2,1]

expected: 0.25

case 5

in: [2,2]

expected: 0.375

Starter codePython

import math


def arcsine_last_visit_probability(n, k):
    # Your code here
    pass

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