problem_2_2.py

from random import random
from scipy import mean
from math import log, pow

import matplotlib.pyplot as plt


def simulate_single(n):
    sample = [random() - 0.5 for _ in range(n)]

    mx = mean(sample)
    tx = 0.5 * (max(sample) + min(sample))

    return pow(mx, 2), pow(tx, 2)


def simulate_estimator(n, K):
    errors = [simulate_single(n) for _ in range(K)]
    total_mx2 = total_tx2 = 0

    for mx2, tx2 in errors:
        total_mx2 += mx2 / K
        total_tx2 += tx2 / K

    return total_mx2, total_tx2


print("mean errors squared:")
print(simulate_estimator(100, 1000))

k = 6

errs = [simulate_estimator(10 ** k, 1000) for k in range(k)]

mxs = [log(x) / log(10) for x, _ in errs]
txs = [log(x) / log(10) for _, x in errs]

plt.plot(range(k), mxs)
plt.plot(range(k), txs)
plt.show()