# Start writing code here...
# 统计常用模块
%matplotlib inline
import numpy as np
import pandas as pd
from scipy import stats
from scipy.stats import norm,chi2,t,f
import matplotlib.pyplot as plt
# import statsmodels.api as sm
# from statsmodels.formula.api import ols
# from statsmodels.graphics.api import interaction_plot, abline_plot
# from statsmodels.stats.anova import anova_lm
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# chapter1 图1-1 p4
x = np.linspace(-0.2,1.2,140)
# plt.plot(x,[0 for i in x],'b--')
# plt.plot([0 for i in x ],x,'b--')
a = np.sin(2*np.pi*x[20:120])
b= np.cos(2*np.pi*x[20:120])
plt.plot(a/2,b/2,'r-')
plt.plot(a/3,b/3,'r-')
plt.text(.4,0.1,'$B$',fontsize = 15)
plt.text(-.45,-0.45,'$S$',fontsize = 15)
plt.text(-.1,-0.1,'$A$',fontsize = 15)
plt.title('fig_1_1')
plt.show()
# chapter1 图1-2 p4
x = np.linspace(-0.2,1.2,140)
# plt.plot(x,[0 for i in x],'b--')
# plt.plot([0 for i in x ],x,'b--')
a = np.sin(2*np.pi*x[20:120])
b= np.cos(2*np.pi*x[20:120])
plt.plot(a/2,b/2,'r-')
plt.plot(a/3+0.3,b/3+0.3,'r-')
x1 = np.arange(-0.5,0.5,0.01)
plt.fill_between(x1,0,np.sqrt(0.25-x1**2),color = 'b',alpha = 0.4)
plt.fill_between(x1,-np.sqrt(0.25-x1**2),0,color = 'b',alpha = 0.4)
x2 = np.arange(-0.5,0.5,0.01)
plt.fill_between(x2+0.3,0.3,np.sqrt(1/9-x2**2)+0.3,color = 'b',alpha = 0.4)
plt.fill_between(x2+0.3,-np.sqrt(1/9-x2**2)+0.3,0.3,color = 'b',alpha = 0.4)
plt.text(.4,0.4,'$B$',fontsize = 15)
plt.text(-.45,-0.45,'$S$',fontsize = 15)
plt.text(-.1,-0.1,'$A$',fontsize = 15)
plt.title('fig_1_2')
plt.show()
# chapter1 图1-2 p4
x = np.linspace(-0.2,1.2,140)
plt.plot(x1,[0 for i in x1],'w-',alpha = 0.3)
plt.plot(x2,[0 for i in x2],'w-',alpha = 0.4)
# plt.plot([0 for i in x ],x,'b--')
a = np.sin(2*np.pi*x[20:120])
b= np.cos(2*np.pi*x[20:120])
plt.plot(a/2,b/2,'r-')
plt.plot(a/3+0.3,b/3+0.3,'r-')
x1 = np.arange(-0.5,0.5,0.01)
plt.fill_between(x1,0,np.sqrt(0.25-x1**2),color = 'b',alpha = 0.4)
plt.fill_between(x1,-np.sqrt(0.25-x1**2),0,color = 'b',alpha = 0.4)
x2 = np.arange(-0.5,0.5,0.01)
plt.fill_between(x2+0.3,0.3,np.sqrt(1/9-x2**2)+0.3,color = 'b',alpha = 0.4)
plt.fill_between(x2+0.3,-np.sqrt(1/9-x2**2)+0.3,0.3,color = 'b',alpha = 0.4)
plt.text(.4,0.4,'$B$',fontsize = 15)
plt.text(-.45,-0.45,'$S$',fontsize = 15)
plt.text(-.1,-0.1,'$A$',fontsize = 15)
plt.title('fig_1_2')
plt.show()
# chapter1 图1-4 p4
x = np.linspace(-0.2,1.2,140)
plt.plot(x1,[0 for i in x1],'w-',alpha = 0.3)
# plt.plot(x2,[0 for i in x2],'w-',alpha = 0.4)
# plt.plot([0 for i in x ],x,'b--')
a = np.sin(2*np.pi*x[20:120])
b= np.cos(2*np.pi*x[20:120])
plt.plot(a/2,b/2,'r-')
plt.plot(a/3+1/3,b/3+1/3,'r-')
x1 = np.arange(-0.5,0.5,0.01)
plt.fill_between(x1,0,np.sqrt(0.25-x1**2),color = 'w')
plt.fill_between(x1,-np.sqrt(0.25-x1**2),0,color = 'w')
x2 = np.arange(-0.5,0.5,0.01)
plt.fill_between(x2+1/3,1/3,np.sqrt(1/9-x2**2)+1/3,color = 'b',alpha = 0.4)
plt.fill_between(x2+1/3,-np.sqrt(1/9-x2**2)+1/3,1/3,color = 'b',alpha = 0.4)
plt.fill_between(x2[:22]+1/3,1/3,np.sqrt(1/9-x2[:22]**2)+1/3,color = 'w')
plt.fill_between(x2[:22]+1/3,-np.sqrt(1/9-x2[:22]**2)+1/3,1/3,color = 'w')
# plt.fill_between(x2[22:80]+1/3,1/3,np.sqrt(1/9-x2[22:80]**2)+1/3,color = 'w')
# plt.fill_between(x2[22:66]+1/3,-np.sqrt(1/9-x2[22:66]**2)+1/3,np.sqrt(1/4-x2[22:66]**2),color = 'w')
plt.fill_between(x1,0,np.sqrt(0.25-x1**2),color = 'w')
plt.plot(x2+1/3,[1/3 for i in x2],'w-',alpha =0.5)
plt.text(.4,0.4,'$A$',fontsize = 15)
plt.text(-.45,-0.45,'$S$',fontsize = 15)
plt.text(-.1,-0.1,'$B$',fontsize = 15)
plt.title('fig_1_4')
plt.show()
# chapter1 图1-2 p4
x = np.linspace(-0.2,1.2,140)
plt.plot(x1,[0 for i in x1],'w-',alpha = 0.3)
# plt.plot(x2,[0 for i in x2],'w-',alpha = 0.4)
# plt.plot([0 for i in x ],x,'b--')
a = np.sin(2*np.pi*x[20:120])
b= np.cos(2*np.pi*x[20:120])
plt.plot(a/2,b/2,'r-')
plt.plot(a/3+1/3,b/3,'r-')
x1 = np.arange(-0.5,0.5,0.01)
plt.fill_between(x1,0,np.sqrt(0.25-x1**2),color = 'w')
plt.fill_between(x1,-np.sqrt(0.25-x1**2),0,color = 'w')
x2 = np.arange(-0.5,0.5,0.01)
plt.fill_between(x2+1/3,0,np.sqrt(1/9-x2**2),color = 'b',alpha = 0.4)
plt.fill_between(x2+1/3,-np.sqrt(1/9-x2**2),0,color = 'b',alpha = 0.4)
plt.fill_between(x2[:55]+1/3,0,np.sqrt(1/9-x2[:55]**2),color = 'w')
plt.fill_between(x2[:55]+1/3,-np.sqrt(1/9-x2[:55]**2),0,color = 'w')
# plt.fill_between(x2[22:80]+1/3,1/3,np.sqrt(1/9-x2[22:80]**2)+1/3,color = 'w')
# plt.fill_between(x2[22:66]+1/3,-np.sqrt(1/9-x2[22:66]**2)+1/3,np.sqrt(1/4-x2[22:66]**2),color = 'w')
plt.fill_between(x1,0,np.sqrt(0.25-x1**2),color = 'w')
plt.plot(x2+1/3,[1/3 for i in x2],'w-',alpha =0.5)
plt.fill_between(x1,-np.sqrt(0.25-x1**2),0,color = 'w')
plt.text(.55,0.,'$A$',fontsize = 15)
plt.text(-.45,-0.45,'$S$',fontsize = 15)
plt.text(-.1,-0.1,'$B$',fontsize = 15)
plt.title('A-B')
plt.show()
# chapter1 图1-3 p4
x = np.linspace(-0.2,1.2,140)
a = np.sin(2*np.pi*x[20:120])
b= np.cos(2*np.pi*x[20:120])
plt.plot(a/2,b/2,'r-')
plt.plot(a/3+1/3,b/3,'r-')
x1 = np.arange(-0.5,0.5,0.01)
x2 = np.arange(-0.5,0.5,0.01)
plt.plot(x2+1/3,[1/3 for i in x2],'w-',alpha =0.5)
plt.fill_between(x1[87:],-np.sqrt(0.25-x1[87:]**2),np.sqrt(0.25-x1[87:]**2),color = 'b')
plt.fill_between(x2[:55]+1/3,-np.sqrt(1/9-x2[:55]**2),np.sqrt(1/9-x2[:55]**2),color = 'b')
plt.text(.55,0.,'$A$',fontsize = 15)
plt.text(-.45,-0.45,'$S$',fontsize = 15)
plt.text(-.1,-0.1,'$B$',fontsize = 15)
plt.title('AB')
plt.show()
# chapter1 图1-5 p4
x = np.linspace(-0.2,1.2,140)
a = np.sin(2*np.pi*x[20:120])
b= np.cos(2*np.pi*x[20:120])
plt.plot(a/2,b/2,'r-')
plt.plot(a/3+1,b/3,'r-')
plt.text(.95,0.,'$A$',fontsize = 15)
plt.text(-.45,-0.45,'$S$',fontsize = 15)
plt.text(-.1,-0.1,'$B$',fontsize = 15)
plt.title('AB=$\phi$')
plt.show()
# chapter1 图1-6 p4
x = np.linspace(-0.2,1.2,140)
a = np.sin(2*np.pi*x[20:120])
b= np.cos(2*np.pi*x[20:120])
plt.plot(a/2,b/2,'r-')
# plt.plot(a/3+1,b/3,'r-')
# plt.text(.95,0.,'$A$',fontsize = 15)
plt.text(-.45,-0.45,'$S$',fontsize = 15)
plt.text(-.1,-0.1,'$A$',fontsize = 15)
plt.title('AB=$\phi$')
plt.show()
# p35 fig2_3
plt.bar(np.arange(20),height=(stats.binom.pmf(np.arange(20),p=0.2,n=20)),width=0.75,alpha=0.75)
plt.show()
# p35 fig2_5
x = np.linspace(-1.2,3.6,480)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x[80:240]],x[80:240],'b--')
plt.plot(x[:20],[0 for i in x[:20]],'b-')
plt.plot(x[20:320],[1/4 for i in x[20:320]],'b-')
plt.plot(x[320:420],[3/4 for i in x[320:420]],'b-')
plt.plot(x[420:],[1 for i in x[420:]],'b-')
plt.text(-1.05,1/4-0.01, '●',fontsize = 9)
plt.text(1.95,3/4-0.01,'●',fontsize = 9)
plt.text(2.95,1-0.01,'●',fontsize = 9)
plt.text(3.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.2,-0.2,'$o$',fontsize = 15)
plt.show()
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
x1 = np.linspace(0,1,100)
a = np.sin(x1*np.pi/2)
b = np.cos(x1*np.pi/2)
plt.plot(a,-b+1,'r-')
plt.plot(x[120:],[1 for i in x[120:]],'r-')
plt.plot(x[20:23],[1 for i in x[20:23]],'b-')
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$F(x)$',fontsize = 15)
plt.text(0.48,-0.1,'$1$')
plt.text(0.98,-0.1,'$2$')
plt.text(-.1,1.0,'$1$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图2-7 p43
x = np.linspace(-1.2,1.2,240)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x[80:] ],x[80:],'b--')
x1 = np.linspace(0,1,100)
a = 0.5*np.sin(x1*np.pi/2)
b = 0.5*np.cos(x1*np.pi/2)
plt.plot(a,-b+0.5,'r-')
plt.plot(-a,-b+0.5,'r-')
y1 = 2*1/np.sqrt(np.pi*2)*np.exp(-(x[:80]+1)**2/2)
y2 = 2*1/np.sqrt(np.pi*2)*np.exp(-(x[160:]-1)**2/2)
plt.plot(x[:80],y1,'r-')
plt.plot(x[160:],y2,'r-')
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
x = np.linspace(-4.2,4.2,840)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x[400:470] ],x[400:470],'b--')
y1 = 1/np.sqrt(np.pi*2)*np.exp(-(x+2)**2/2)
y2 = 1/np.sqrt(np.pi*2)*np.exp(-(x-2)**2/2)
plt.plot(x,y1,'b-')
plt.plot(x,y2,'r-')
plt.plot([-2 for i in x[400:470]],x[400:470],'b--')
plt.plot([2 for i in x[400:470]],x[400:470],'b--')
plt.text(4.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,0.5,'$y$',fontsize = 15)
plt.text(-.35,-0.05,'$o$',fontsize = 15)
plt.show()
x = np.linspace(-4.2,4.2,840)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x[400:470] ],x[400:470],'b--')
y1 = 1/np.sqrt(np.pi*2)*np.exp(-(x+2)**2/2)
y2 = 1/np.sqrt(np.pi*2)*np.exp(-(x-2)**2/2)
plt.plot(x,y1,'b-')
plt.plot(x,y2,'r-')
plt.plot([-2 for i in x[400:470]],x[400:470],'b--')
plt.plot([2 for i in x[400:470]],x[400:470],'b--')
plt.text(4.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,0.5,'$y$',fontsize = 15)
plt.text(-.35,-0.05,'$o$',fontsize = 15)
plt.show()
fig = plt.figure(figsize=(12,8))
x = np.linspace(-0.5,4.3,480)
y = 1/np.sqrt(np.pi*2)*np.exp(-(x-2)**2/2)
y1 = 1/np.sqrt(np.pi*4)*np.exp(-(x-2)**2/4)
y2 = 1/np.sqrt(np.pi*0.5)*np.exp(-(x-2)**2)
plt.plot(x,y,'b-')
plt.plot(x,y1,'r-')
plt.plot(x,y2,'y-')
plt.plot([0 for i in x[:130]],x[:130],'b--')
plt.plot(x,[0 for i in x],'b--')
plt.plot(x[50:250],[0.272 for i in x[50:250]],'b--')
plt.plot(x[50:250],[0.4 for i in x[50:250]],'b--')
plt.plot(x[50:250],[0.8 for i in x[50:250]],'b--')
plt.plot([2 for i in x[50:130]],x[50:130],'b-')
plt.text(-0.5,0.26,'0.266')
plt.text(-0.5,0.39,'0.399')
plt.text(-0.5,0.79,'0.798')
plt.text(1.95,-0.08,'$\mu$',fontsize = 15)
plt.text(-0.1,0.82,'$f(x)$')
plt.show()
# 图 2_14
x = np.linspace(-3.2,3.2,640)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x[300:420] ],x[300:420],'b--')
plt.plot(x,norm.cdf(x),'b-')
plt.text(3.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.,'$F(x)$',fontsize = 15)
plt.text(-.2,-0.1,'$o$',fontsize = 15)
plt.text(-.6,0.5,'$0.5$',fontsize = 15)
plt.show()
# 图 2_15
x = np.linspace(-3.2,3.2,640)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x[300:375] ],x[300:375],'b--')
plt.plot(x,norm.pdf(x),'b-')
plt.plot([-1 for i in x[320:345]],x[320:345],'b--')
plt.plot([1 for i in x[320:345]],x[320:345],'b--')
plt.text(3.2,-0.1,'$x$',fontsize = 15)
plt.text(-.6,.5,'$\phi(x)$',fontsize = 15)
plt.text(-.2,-0.1,'$o$',fontsize = 15)
# plt.text(-.6,0.5,'$0.5$',fontsize = 15)
plt.show()
# 图 2_16
fig = plt.figure(figsize=(12,8))
x = np.linspace(-3.2,3.2,640)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x[300:375] ],x[300:375],'b--')
plt.plot(x,norm.pdf(x),'b-')
plt.plot([-0.7 for i in x[320:350]],x[320:350],'b--')
plt.plot([0.7 for i in x[320:350]],x[320:350],'b--')
plt.plot([-2.1 for i in x[320:325]],x[320:325],'b--')
plt.plot([2.1 for i in x[320:325]],x[320:325],'b--')
plt.plot([-1.4 for i in x[320:335]],x[320:335],'b--')
plt.plot([1.4 for i in x[320:335]],x[320:335],'b--')
plt.text(3.2,-0.1,'$x$',fontsize = 15)
plt.text(-.4,.5,'$\phi(x)$',fontsize = 15)
plt.text(-.15,-0.02,'$o$',fontsize = 15)
# plt.text(-.6,0.5,'$0.5$',fontsize = 15)
plt.text(-2.2,-0.02,'$\mu-3\sigma$')
plt.text(2.,-0.02,'$\mu+3\sigma$')
plt.text(-1.5,-0.02,'$\mu-2\sigma$')
plt.text(1.4,-0.02,'$\mu+2\sigma$')
plt.text(-0.8,-0.02,'$\mu-\sigma$')
plt.text(0.7,-0.02,'$\mu+\sigma$')
plt.show()
# 图 2_17
x = np.linspace(-3.2,3.2,640)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x[300:375] ],x[300:375],'b--')
plt.plot(x,norm.pdf(x),'b-')
# plt.plot([-1 for i in x[320:345]],x[320:345],'b--')
plt.plot([2 for i in x[320:325]],x[320:325],'b--')
plt.fill_between(x[515:],0,norm.pdf(x[515:]),color= 'r')
plt.text(2.5,0.1,u'\u03B1',fontsize = 15)
plt.arrow(2.5,0.1,-0.25,-0.05)
plt.text(3.2,-0.1,'$x$',fontsize = 15)
plt.text(-.6,.5,'$\phi(x)$',fontsize = 15)
plt.text(-.3,-0.05,'$o$',fontsize = 15)
# plt.text(-.6,0.5,'$0.5$',fontsize = 15)
plt.show()
# 图3-1
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
x1 = np.arange(0,1,0.01)
a = 0.2*np.sin(x1*2*np.pi)
b = 0.2*np.cos(x1*2*np.pi)
plt.plot(a+0.3,b+0.5,'r-')
plt.plot(a+0.9,b+0.22,'r-')
plt.plot(a+0.9,b+0.7,'r-')
plt.arrow(0.3,.5,0.6,0.2)
plt.arrow(0.3,.5,0.6,-0.3)
plt.text(0.25,0.5,'$e$')
plt.text(0.9,0.2,'$Y(e)$',fontsize =15)
plt.text(0.9,0.7,'$X(e)$',fontsize = 15)
plt.text(0.2,0.35,'$S$',fontsize = 15)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-2
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.fill_between(x[:120],-0.2,1,color = 'b',alpha = 0.4)
plt.text(1,1,'$(x,y)$')
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-3
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x[40:120],[1 for i in x[40:120]],'b-')
plt.plot(x[40:120],[0.5 for i in x[40:120]],'b-')
plt.plot(x[20:40],[1 for i in x[20:40]],'b--')
plt.plot(x[20:40],[0.5 for i in x[20:40]],'b--')
plt.plot([1 for i in x[70:120]],x[70:120],'b-')
plt.plot([0.2 for i in x[70:120]],x[70:120],'b-')
plt.plot([1 for i in x[20:70]],x[20:70],'b--')
plt.plot([0.2 for i in x[20:70]],x[20:70],'b--')
plt.text(0.95,-0.1,'$x_2$',fontsize = 15)
plt.text(0.15,-0.1,'$x_1$',fontsize = 15)
plt.text(-.1,1,'$y_2$',fontsize = 15)
plt.text(-.1,.5,'$y_1$',fontsize = 15)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
x = np.linspace(-1.2,1.2,240)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x,x,'b-')
plt.fill_between(x,-1.2,x,color = 'y',alpha = 0.3)
plt.text(0.4,-0.4,'$G$',fontsize = 20)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-5
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x[20:],x[20:],'b-')
plt.plot(x[20:130],x[20:130]**2,'g-')
plt.text(0.5,0.6,'$y=x$',rotation = 30)
plt.text(0.5,0.2,'$y=x^2$',rotation = 30)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-5
x = np.linspace(-1.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
x1 = np.arange(0,1,0.01)
a = np.sin(x1*np.pi*2)
b = np.cos(x1*np.pi*2)
plt.plot(a,b,'r-')
plt.plot([0.5 for i in x1[:86]],x1[:86],'b--')
plt.plot([0.5 for i in x1[:86]],-x1[:86],'b--')
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-0.1,1.,'$1$',fontsize = 15)
plt.text(-0.2,-1.,'$-1$',fontsize = 15)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-5（2）
x = np.linspace(-1.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
x1 = np.arange(0,1,0.01)
a = np.sin(x1*np.pi*2)
b = np.cos(x1*np.pi*2)
plt.plot(a,b,'r-')
plt.plot(x1[:86],[0.5 for i in x1[:86]],'b--')
plt.plot(-x1[:86],[0.5 for i in x1[:86]],'b--')
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(1.,-0.1,'$1$',fontsize = 15)
plt.text(-1.,-0.1,'$-1$',fontsize = 15)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-3
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x[40:120],[1 for i in x[40:120]],'b-')
plt.plot(x[40:120],[0.5 for i in x[40:120]],'b-')
plt.plot(x[20:22],[1 for i in x[20:22]],'b--')
plt.plot(x[20:22],[0.5 for i in x[20:22]],'b--')
plt.plot([1 for i in x[70:120]],x[70:120],'b-')
plt.plot([0.2 for i in x[70:120]],x[70:120],'b-')
plt.plot([1 for i in x[20:22]],x[20:22],'b--')
plt.plot([0.2 for i in x[20:22]],x[20:22],'b--')
plt.plot(x[40:70],x[40:70]+0.5,'r-')
plt.plot(x[40:65],x[40:65]+0.55,'b-')
plt.plot(x[40:60],x[40:60]+0.6,'r-')
plt.text(0.95,-0.1,'$12$',fontsize = 15)
plt.text(0.15,-0.1,'$8$',fontsize = 15)
plt.text(-.1,1,'$9$',fontsize = 15)
plt.text(-.1,.5,'$7$',fontsize = 15)
plt.text(0.3,0.7,'$G$',fontsize = 15)
plt.text(0.14,1,'$A$')
plt.text(0.14,0.8,'$B^{1}$')
plt.text(0.14,0.65,'$B$')
plt.text(0.5,1.02,'$C$')
plt.text(0.38,1.02,'$C^{1}$')
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-9
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x,1-x,'b-')
plt.fill_between(x,-0.2,1-x,color = 'y',alpha = 0.3)
plt.text(0.4,0.5,'$x+y = z$',rotation = -30)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-9
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x[:120],0.8-x[:120],'b-')
plt.fill_between(x[:120],-0.2,0.8-x[:120],color = 'y',alpha = 0.3)
plt.text(0.3,0.5,'$x+y = z$',rotation = -30)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-10
x = np.linspace(-0.2,1.6,160)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x[20:],[0.6 for i in x[20:]],'b-')
plt.plot(x[20:100],x[20:100],'b-')
plt.plot(0.6 + x[20:90],x[20:90],'b-')
plt.plot([0.6 for i in x[20:70]],x[20:70],'b--')
plt.plot([1.2 for i in x[20:70]],x[20:70],'b--')
plt.fill_between(x[20:70],0,x[20:70],color = 'y',alpha = 0.4)
plt.fill_between(x[70:125],x[70:125]-0.6,0.6,color = 'b',alpha = 0.4)
plt.text(0.15,0.63,'$x = 10$',fontsize =15)
plt.text(0.6,0.7,'$x=z$',rotation = 35,fontsize =15)
plt.text(1.2,0.7,'$x=z-10$',rotation = 35,fontsize =15)
plt.text(0.5,-0.1,'$10$',fontsize = 15)
plt.text(1.2,-0.1,'$20$',fontsize = 15)
plt.text(1.6,-0.1,'$z$',fontsize = 15)
plt.text(-.1,1.4,'$x$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图 3-11
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x[20:],x[20:],'b-')
plt.fill_between(x[20:],0,x[20:],color = 'b',alpha = 0.4)
plt.text(1.2,-0.1,'$z$',fontsize = 15)
plt.text(-.1,1.2,'$x$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图 3-12
x = np.linspace(-1.2,1.2,240)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x[20:],x[20:],'b-')
plt.fill_between(x[:120],x[:120],1,color = 'b',alpha = 0.4)
plt.fill_between(x[120:],-1,x[120:],color = 'b',alpha = 0.4)
plt.text(0.5,0.6,'$y = zx$',rotation =30)
plt.text(-0.7,0.5,'$G_1$',fontsize = 15)
plt.text(0.7,-0.5,'$G_2$',fontsize = 15)
plt.text(0.7,-0.9,'$z>0$',fontsize = 15)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图 3-12
x = np.linspace(-1.2,1.2,240)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.plot(x[70:180],-2*x[70:180],'b-')
plt.fill_between(x[70:120],-2*x[70:120],1,color = 'b',alpha = 0.4)
plt.fill_between(x[120:170],-1,-2*x[120:170],color = 'b',alpha = 0.4)
plt.text(-0.7,0.5,'$y = zx$',rotation =-55,fontsize = 15)
plt.text(-0.2,0.5,'$G_1$',fontsize = 15)
plt.text(0.1,-0.5,'$G_2$',fontsize = 15)
plt.text(0.1,-0.9,'$z<0$',fontsize = 15)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-13
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.fill_between(x[50:70],0.4,0.6,color = 'b')
plt.fill_between(x[90:110],0.4,0.6,color = 'b')
plt.arrow(0,0.5,0.27,0,head_width = 0.02)
plt.arrow(0.5,0.5,0.2,0)
plt.arrow(0.9,0.5,0.27,0,head_width = 0.02)
plt.text(0.35,0.48,'$X$',fontsize = 15,color ='w')
plt.text(0.35,0.28,'$L_1$',fontsize = 15)
plt.text(0.75,0.48,'$Y$',fontsize = 15,color ='w')
plt.text(0.75,0.28,'$L_2$',fontsize = 15)
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-13
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.fill_between(x[50:70],0.4,0.6,color = 'b')
plt.fill_between(x[50:70],0.7,0.9,color = 'b')
plt.arrow(0,0.8,0.12,0,head_width = 0.02)
plt.arrow(0.5,0.5,0.2,0)
plt.arrow(0.5,0.8,0.5,0,head_width = 0.02)
plt.arrow(0.15,0.5,0.19,0)
plt.arrow(0.1,0.8,0.19,0)
plt.arrow(0.7,0.5,0.,0.3)
plt.arrow(0.15,0.5,0.,0.3)
plt.text(0.35,0.8,'$Y$',fontsize = 15,color ='w')
plt.text(0.1,0.9,'$L_1$',fontsize = 15)
plt.text(0.35,0.48,'$X$',fontsize = 15,color ='w')
plt.text(0.1,0.28,'$L_2$',fontsize = 15)
plt.text(0.12,0.8,u'\u0149')
plt.text(0.67,0.8,u'\u0149')
# plt.text(0.67,0.8,u'\u41457🞄')
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图3-13
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
plt.fill_between(x[50:70],0.4,0.6,color = 'b')
plt.fill_between(x[50:70],0.7,0.9,color = 'b')
plt.arrow(0,0.8,0.12,0,head_width = 0.02)
plt.arrow(0.5,0.5,0.2,0)
plt.arrow(0.5,0.8,0.5,0,head_width = 0.02)
plt.arrow(0.15,0.5,0.19,0)
plt.arrow(0.1,0.8,0.19,0)
plt.arrow(0.7,0.5,0.,0.3)
plt.arrow(0.15,0.5,0.,0.1)
plt.arrow(0.15,0.7,0.,0.1)
plt.arrow(0.15,0.6,0.05,0.1)
plt.text(0.35,0.8,'$Y$',fontsize = 15,color ='w')
plt.text(0.1,0.9,'$L_1$',fontsize = 15)
plt.text(0.35,0.48,'$X$',fontsize = 15,color ='w')
plt.text(0.1,0.28,'$L_2$',fontsize = 15)
plt.text(0.12,0.8,u'\u0149')
plt.text(0.67,0.8,u'\u0149')
# plt.text(0.67,0.8,u'\u1F784')
# plt.text(0.67,0.8,u'\u41457🞄')
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图4-1
x = np.linspace(-0.2,1.2,140)
plt.plot(x,[0 for i in x],'b--')
plt.plot([0 for i in x ],x,'b--')
x1 = np.arange(0,1,0.01)
a = 0.3*np.sin(x1*2*np.pi)
b = 0.3*np.cos(x1*2*np.pi)
plt.plot(a+0.6,b+0.6,'r-')
plt.arrow(0.2,0.2,0.8,0)
plt.arrow(0.2,1,0.8,0)
plt.arrow(0.2,0.2,0,0.8)
plt.arrow(1,0.2,0,0.8)
plt.plot()
plt.text(0.6,0.6,'$e_1$')
plt.text(0.85,0.35,'$e_2$')
plt.text(1.1,0.35,'$e_0$')
plt.text(1.2,-0.1,'$x$',fontsize = 15)
plt.text(-.1,1.2,'$y$',fontsize = 15)
plt.text(-.1,-0.1,'$o$',fontsize = 15)
plt.show()
# 图4-2
x = np.linspace(-3.2,3.2,640)
plt.plot(x,[0 for i in x],'b--')
plt.plot([-0.8 for i in x[300:380] ],x[300:380],'b--')
plt.plot(x,norm.pdf(x),'r-')
plt.fill_between(x[540:],0,norm.pdf(x[540:]),color = 'b',alpha = 0.5)
plt.fill_between(x[:100],0,norm.pdf(x[:100]),color = 'b',alpha = 0.5)
# plt.text(2.5,0.1,u'\u03B1')
plt.text(-0.,-0.05,'$\mu$')
plt.text(0,-0.01,u'\u1F78',fontsize = 12)
plt.text(2,-0.05,'$\mu+\epsilon$')
plt.text(-2.3,-0.05,'$\mu-\epsilon$')
plt.text(3.2,-0.1,'$x$',fontsize = 15)
plt.text(-1.1,0.6,'$y$',fontsize = 15)
plt.text(-1.1,-0.05,'$o$',fontsize = 15)
plt.show()
