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Matlab and Python are commonly used tools in data processing, probability theory is a very important foundation in quantitative model, and central limit theorem is a very important theory in probability theory.

The central limit theorem is defined as:

Let the random sequence {Xi} be independent and identically distributed, with a common mathematical expectation u and variance σ ^ 2.

Standardize the definition of Sn

Cymbals

Converge to the standard normal distribution according to the distribution. That is, for any x

Phellodendron mandshurica (Thunb.)

Phellodendron mandshurica (Thunb.)

Here Φ (x) is the distribution function of the standard normal distribution.

For binomial distribution

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When n →∞, the distribution shape of Sn is very similar to that of normal distribution.

So, today we're going to look at the change in the shape of Sn as n grows up.

Matlab dynamic diagram:

Python dynamic diagram:

Matlab Code:

Clear all

Close all

Clc

%% binomial distribution

P = 0.6

N = 1000

Psn = zeros (1)

If 1

H3 = plot (0purn Psn)

Grid on

% axis ([0n 00.05])

Axis ([1 100 0 0.09])

For iTunes 100ln

For k = 0PUR I

Psn (KPY 1) = nchoosek (iMagol k) * (p ^ k) * ((1murp) ^ (iMurk))

End

Set (floor (iTunes 0.6)-50:floor (item0.6) + 50)

Drawnow

Grid on

Pause (0. 01)

End

End

Python Code:

#-*-coding: utf-8-*-

"

File Name: central_limit_theorem1.py

Description:

Author: Z270

Date: 2018-8-30

Change Activity:

2018-8-30:

"

Import numpy as np

From scipy.special import comb

Import matplotlib.pyplot as plt

P = 0.6

N = 1000

Psn = np.zeros (nasty 1)

Plt.figure (figsize= (8,6), dpi=80)

# turn on interactive mode

Plt.ion ()

For i in range (10010):

For k in range (iTun1):

Psn [k] = comb (imam k) * (pumped quok) * ((1MIML p) * * (iMel k))

Plt.cla ()

Plt.grid (True)

Plt.xlim (1100)

Plt.ylim (0Pol 0.09)

Plt.plot (range (1102), Psn [int (np.floor (0.6))-50:int (np.floor (0.6)) + 51], linewidth = 2.0)

Plt.pause (0.1)

Print (I)

Plt.ioff ()

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