中心极限定理

中心极限定理

中心极限定理指的是给定一个任意分布的总体。我每次从这些总体中随机抽取 n 个抽样，一共抽 m 次。 然后把这 m 组抽样分别求出平均值。 这些平均值的分布接近正态分布。

实验验证

写了代码 做实验 发现真的是这样。。
这里简单的用了均匀分布

import numpy as np
import matplotlib.pyplot as plt

random_data = np.random.randint(1,7,10000)
print random_data.mean()
print random_data.std()
number = [0,0,0,0,0,0]
for x in random_data:
    number[x-1] += 1
Y = np.array(number)
X = np.array([1,2,3,4,5,6])
plt.figure()
plt.bar(X,Y)

#samples = []
samples_mean = []
#samples_std = []
for i in range(0,1000):
    sample = []
    for j in range(0,50):
        sample.append(random_data[int(np.random.random() * len(random_data))])
    sample_np = np.array(sample)
    samples_mean.append(sample_np.mean())
    #samples_std.append(sample_np.std())
    #samples.append(sample_np)  
samples_mean_np = np.array(samples_mean)
#samples_std_np = np.array(samples_std)

plt.figure()
number2 = [0,0,0,0,0,0,0]
for x in samples_mean:
    if x >= 2.8 and x < 3.0:
        number2[0] += 1
    if x >= 3.0 and x < 3.2:
        number2[1] += 1
    if x >= 3.2 and x < 3.4:
        number2[2] += 1
    if x >= 3.4 and x < 3.6:
        number2[3] += 1
    if x >= 3.6 and x < 3.8:
        number2[4] += 1
    if x >= 3.8 and x < 4.0:
        number2[5] += 1
    if x >= 4.0 and x < 4.2:
        number2[6] += 1


Y2 = np.array(number2)
X2 = np.arange(1,8,1)
plt.bar(X2,Y2)
plt.xticks(X2, ('2.9', '3.1', '3.3', '3.5', '3.7','3.9','4.1'))
plt.show()

实验结果

参考：
https://zhuanlan.zhihu.com/p/25241653