Ehrenfest Return Time

Problem

Expected return time to state 0 of the Ehrenfest chain with d balls, which equals the reciprocal of its stationary probability 2^(-d):

E[T] = 2^d.

Return 0 for negative d.

Hint

For a finite irreducible chain, the mean return time to a state is 1 over its stationary probability.

case 1

in: [0]

expected: 1

case 2

in: [1]

expected: 2

case 3

in: [4]

expected: 16

case 4

in: [10]

expected: 1024

Starter codePython

def ehrenfest_return_time(d):
    # Your code here
    pass

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