Demonstrate Law of Large Numbers with Sampling

import numpy as np
from typing import Dict, List

def law_of_large_numbers(
    distribution: str = "normal",
    params: dict = None,
    sample_sizes: List[int] = None,
    n_trials: int = 1000,
    seed: int = 42
) -> Dict:
    np.random.seed(seed)

    if params is None:
        params = {"loc": 5.0, "scale": 2.0}
    if sample_sizes is None:
        sample_sizes = [10, 50, 100, 500, 1000, 5000, 10000]

    # Determine true mean
    if distribution == "normal":
        true_mean = params.get("loc", 0)
        sampler = lambda size: np.random.normal(
            params.get("loc", 0), params.get("scale", 1), size
        )
    elif distribution == "uniform":
        low, high = params.get("low", 0), params.get("high", 1)
        true_mean = (low + high) / 2
        sampler = lambda size: np.random.uniform(low, high, size)
    elif distribution == "exponential":
        scale = params.get("scale", 1.0)
        true_mean = scale
        sampler = lambda size: np.random.exponential(scale, size)
    else:
        raise ValueError(f"Unsupported distribution: {distribution}")

    results = []
    for n in sample_sizes:
        means = [float(np.mean(sampler(n))) for _ in range(n_trials)]
        avg_mean = np.mean(means)
        std_mean = np.std(means)
        results.append({
            "sample_size": n,
            "average_sample_mean": round(float(avg_mean), 4),
            "std_of_means": round(float(std_mean), 4),
            "error": round(float(abs(avg_mean - true_mean)), 6)
        })

    return {
        "true_mean": true_mean,
        "distribution": distribution,
        "results": results
    }