# 依赖: numpy
import numpy as np

rng = np.random.default_rng(42)
N = 200_000                                   # 迭代次数必须写进论文
x = rng.uniform(0.0, 1.0, N)
y = rng.uniform(0.0, 1.0, N)

hit = (x ** 2 + y ** 2) <= 1.0
p = hit.mean()
se = np.sqrt(p * (1 - p) / N)                 # 必须给出置信区间
print(f'估计值 = {4 * p:.4f}  95% CI = ± {1.96 * 4 * se:.4f}  (N={N})')