Drawing three ways Gaussian Distribution Curve

There are three mathematical symbols in a Gaussian distribution, the first to explain the meaning of the three mathematical symbols, and then explain to derive ideas and derivation of this formula.
Three symbols \ (\ mu, \ sigma, e \) were called the average value (also known mathematical expectation) Mathematically, standard deviation, a natural number. That is:
the average value (also known mathematical expectation): \ (\ MU \)
standard deviation: \ (\ Sigma \)
a natural number: \ (E \)

Gaussian distribution mathematical formula

\ [f (x) = \ frac {1} {\ sqrt {2 \ pi \ sigma}} \ cdot e ^ {\ frac {- (x- \ mu) ^ 2} {2 \ sigma ^ 2}} \ ]
expected (average): μ
standard deviation \ (: [sigma] \) ,
the variance \ (σ ^ 2 \) is.
When \ (\ mu = 0 \) and \ (\ sigma = 1 \) when referred to: standard normal distribution .

\[f(x)=\frac{1}{ \sqrt{2} } \cdot e^{ \frac{-(x)^2}{2}}\]

Drawing three ways Gaussian Distribution Curve

GGB draw

Python draw

import numpy as np
import matplotlib.pyplot as plt
import math
# Python实现正态分布
# 绘制正态分布概率密度函数
u = 0   # 均值μ
sig = math.sqrt(2)  # 标准差δ

x = np.linspace(u - 3*sig, u + 3*sig, 50)
x_01 = np.linspace(u - 6 * sig, u + 6 * sig, 50)
y_sig = np.exp(-(x - u) ** 2 /(2* sig **2))/(math.sqrt(2*math.pi)*sig)


plt.plot(x, y_sig, "r-", linewidth=2)
plt.grid(True)
plt.show()

Matlab

Drawing command matlab normal probability density function of the image is normpdf, call format normpdf function is normpdf (x, mu, sigma), where mu is 0, sigma is 1, is a standard normal distribution.

x=-3:0.1:3;
y=normpdf(x,0,1);
plot(x,y,'r')