Introduction

This notebook is used to generate the various continuous PDFs and CDFs in the lecture notes.



In [6]:

    
from __future__ import division

import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl

mpl.rcParams['lines.linewidth'] = 2
mpl.rcParams['lines.color'] = 'r'
mpl.rcParams['axes.titlesize'] = 32
mpl.rcParams['axes.labelsize'] = 24 
mpl.rcParams['axes.labelsize'] = 24 
mpl.rcParams['xtick.labelsize'] = 24 
mpl.rcParams['ytick.labelsize'] = 24 

%matplotlib inline

def make_plot(x, y, xlabel="$x$", ylabel="$f_X(x)$"):
    plt.figure(figsize=(12, 8))
    plt.plot(x, y, 'k-', linewidth=3)
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    plt.xlim([min(x), max(x)])



In [7]:

    
import math

c = math.sqrt(2/3)

make_plot([0, c, c, 2*c, 2*c, 2*c + 1], [0, 0, c, 2*c, 0, 0])



In [8]:

    
x = np.arange(c, 2*c, c/100)
y = (x**2 - c**2)/2
x = [0] + list(x) + [2]
y = [0] + list(y) + [1]
make_plot(x, y, ylabel="$F_X(x)$")



In [9]:

    
#Exponential
x = np.arange(0, 10, 0.01)
y = np.exp(-1*x)
make_plot(x, y, ylabel="$f_T(t) / \lambda$", xlabel="$t$")



In [10]:

    
y = 1 - np.exp(-x)
make_plot(x, y, ylabel="$F_T(t)$", xlabel="$t$")



In [10]: