Absorbing Probability Two-State

Problem

Absorption in a two-state Markov chain where state 0 is absorbing.

From state 1 the chain moves to state 0 with probability p and otherwise stays in state 1. Starting from state 1, return [probability of eventual absorption, expected number of steps]: [1.0, 1.0 / p] when 0 < p < 1, [1.0, 1.0] when p >= 1, and [0.0, -1.0] when p <= 0.

Hint

Absorption follows a geometric distribution with success probability p.

Test cases

case 1

in: [0.5]

expected: [1,2]

case 2

in: [0.25]

expected: [1,4]

case 3

in: [1]

expected: [1,1]

case 4

in: [0]

expected: [0,-1]

case 5

in: [0.1]

expected: [1,10]

Starter codePython

def absorbing_probability_two_state(p):
    # Your code here
    pass

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