Exponential Mixture Composition (Seeded)

Problem

Sample from a two-component exponential mixture using the composition method: with probability p1 draw from Exponential(lam1), otherwise from Exponential(lam2). Return the seeded sample mean over n draws. Return 0.0 for invalid inputs.

Hint

Choose the component first, then sample from it with a second uniform.

Test cases

case 1

in: [1,2,0.5,20000,42]

expected: 0.7507352428918592

case 2

in: [1,2,0.5,20000,7]

expected: 0.7461103728816006

case 3

in: [3,0.5,0.7,10000,1]

expected: 0.8352886808240652

case 4

in: [1,2,0.5,0,0]

expected: 0

Starter codePython

import math
import random


def composition_sample_mean(lam1, lam2, p1, n, seed):
    # Your code here
    pass

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