Optional Stopping Inflation (Seeded)

Problem

Optional stopping can inflate the largest z-score. Estimate E[max of n independent standard normal variables] by simulation: for each of trials experiments draw n standard normals with a seeded Box-Muller transform and average the maximum. Return 0.0 for n <= 0 or trials <= 0.

Hint

Use 1 - rng.random() in the Box-Muller transform so the logarithm is always defined.

Test cases

case 1

in: [10,2000,42]

expected: 1.5311661530535472

case 2

in: [100,1000,7]

expected: 2.5290880063226346

case 3

in: [1,500,0]

expected: -0.03259471581671577

case 4

in: [0,5,1]

expected: 0

Starter codePython

import math
import random


def max_of_normals_expected_simulation(n, trials, seed):
    # Your code here
    pass

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