Antithetic Variates Estimate (Seeded)

Problem

Estimate E[exp(U)] for U uniform on (0, 1), whose exact value is e - 1, using n antithetic pairs. For each pair draw u with random.Random(seed), average exp(u) and exp(1 - u), and return the overall mean.

Return 0.0 for n <= 0.

Hint

The two values of each pair are negatively correlated because exp is monotone.

Test cases

case 1

in: [20000,42]

expected: 1.718325754686535

case 2

in: [20000,7]

expected: 1.7184331002239301

case 3

in: [100,0]

expected: 1.7132295901718049

case 4

in: [0,5]

expected: 0

Starter codePython

import math
import random


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

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