15  The Maximum Is a Different Kind of Statistic

Introduces \(M_n = \max(X_1, \ldots, X_n)\) as an object worth studying in its own right:

def max_distribution_experiment(sample_fn, n, trials=2000):
    return [max(sample_fn() for _ in range(n)) for _ in range(trials)]

For independent draws, \(P(M_n \le x) = F(x)^n\) — derived, then verified by comparing the simulated histogram of maxima against the theoretical curve for a simple case (uniform data).