Branching Process Mean Growth

Problem

For a branching process with offspring distribution probs (probs[k] = P(k offspring)), the mean offspring number is mu = sum(k * probs[k]). Return the expected population size in generation n:

E[Z_n] = mu^n.

Return 0.0 for an empty distribution or negative n.

Hint

Take the expectation of the generation size one step at a time.

Test cases

case 1

in: [[0.5,0.5],3]

expected: 0.125

case 2

in: [[1],5]

expected: 0

case 3

in: [[0.2,0.8],2]

expected: 0.6400000000000001

case 4

in: [[0.1,0.2,0.7],2]

expected: 2.5599999999999996

Starter codePython

def branching_mean_growth(probs, n):
    # Your code here
    pass

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