How to verify the central limit theorem in python

Python method to verify the central limit theorem: first simulate randomly throwing dice 1000 times and observe the average; then simulate throwing dice ten times and draw a picture to see their distribution; finally simulate 1000 groups, and each group throws 50 times, and take the average of each group to see the distribution.

Python method to verify the central limit theorem:

Central limit theorem:

From a given population obeying any distribution, n samples are drawn each time, m times in total. Then average the values ​​of each group of m, and the average value of each group will obey an approximately normal distribution.

• First simulate randomly throwing dice 1000 times and observe the average value.

import numpy as np
a = np.random.randint(1,7,1000)print(a)a.mean()

Output result:

As you can see, the average value is taken after throwing 1000 times (note: this average value is slightly different every time, because is randomly selected) is close to 3.5 (3.5=1/6*(1 2 3 4 5 6)).
Then, simulate throwing 10,000 times again, and take the average value

You can see that the result is getting closer to 3.5

• Then simulate throwing ten times, and then Draw a picture to see their distribution

sample = []for i in range(10):
    sample.append(a[int(np.random.random()*len(a))]) #从a里面随机抽plt.figure(figsize=(20,10),dpi=100)plt.bar(sample,range(len(sample)))plt.show()

It can be seen that the distribution is not very uniform.

• Then simulate 1,000 groups, each group is thrown 50 times, and then take the average of each group to see the distribution.

sample_mean=[]sample_std=[]samples=[]for i in range(1000):
    sample=[] #每组一个列表
    for j in range(60):
        sample.append(a[int(np.random.random()*len(a))])#模拟抛50次
    sample = np.array(sample) #转化为array数组，便于处理
    sample_mean.append(sample.mean())
    sample_std.append(sample.std())
    samples.append(sample)sample_mean_np = np.array(sample_mean)sample_std_np = np.array(sample_std)print(sample_mean_np)

plt.figure(figsize=(20,10),dpi=80)d =0.1 num_bins = (max(sample_mean_np)-min(sample_mean_np))//d
plt.hist(sample_mean_np,num_bins) #绘制频率分布图

It can be seen that the average value of each group obeys the normal distribution.

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