What is the dynamic graph method of drawing binomial distribution by matlab python?
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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
Cymbals
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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