MediumProbabilitypr-129

Ehrenfest Stationary Distribution

Problem

Stationary distribution of the Ehrenfest chain with d balls, which is Binomial(d, 1/2):

pi[k] = C(d, k) / 2^d for k = 0..d.

Return the list of probabilities for k in increasing order.

Hint

Each ball independently ends up in the left box half the time at stationarity.

case 1

in: [0]

expected: [1]

case 2

in: [1]

expected: [0.5,0.5]

case 3

in: [2]

expected: [0.25,0.5,0.25]

case 4

in: [4]

expected: [0.0625,0.25,0.375,0.25,0.0625]

Starter codePython

import math


def ehrenfest_stationary_distribution(d):
    # Your code here
    pass

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