Introduction to Probability
Preface
I Basics of Probability
1 Probability and Counting
2 The Factorial
3 Box Models and Combinations
4 Sampling With Replacement
5 Double Counting
6 Conditional Probability
7 Independence
8 Law of Total Probability
9 Bayes’ Theorem
II Discrete Probability
10 Random Variables
11 Cumulative Distribution Functions
- Theory
- Examples
12 Hypergeometric Distribution
13 Binomial Distribution
14 Geometric Distribution
15 Negative Binomial Distribution
16 Poisson Distribution
17 Poisson Process
18 Joint Distributions
19 Marginal Distributions
20 Conditional Distributions
21 Sums of Random Variables
22 Expected Value
23 Expected Value and Infinity
- 23.1 Pascal’s Wager
- 23.2 St. Petersburg Paradox
24 LOTUS
25 2D LOTUS
- Theory
- Essential Practice
26 Linearity of Expectation
27 Expected Value of a Product
- Theory
- Essential Practice
28 Variance
29 Covariance
30 Properties of Covariance
31 Random Walk
- Theory
- Essential Practice
32 Law of Large Numbers
III Continuous Probability
33 Continuous Random Variables
34 Uniform Distribution
35 Exponential Distribution
36 Transformations
37 Expected Value of Continuous Random Variables
- Theory
- Essential Practice
38 LOTUS for Continuous Random Variables
- Theory
- Essential Practice
39 Variance of Continuous Random Variables
40 Normal Distribution
41 Joint Continuous Distributions
42 Marginal Continuous Distributions
43 Expectations of Joint Continuous Distributions
- Theory
- Essential Practice
44 Covariance of Continuous Random Variables
- Theory
- Essential Practice
45 Sums of Continuous Random Variables
- Theory
- Essential Practice
46 Central Limit Theorem
IV Random Processes
47 Random Processes
48 Examples of Random Processes
49 Brownian Motion
- Brownian Motion as the Limit of a Random Walk
- Essential Practice
50 Mean Function
- Theory
- Essential Practice
51 Variance Function
- Theory
- Essential Practice
52 Autocovariance Function
- Theory
- Essential Practice
53 Stationary Processes
V Random Signal Processing
54 Autocorrelation Function
- Theory
- Essential Practice
55 Power of a Stationary Process
56 Power Spectral Density
57 LTI Filters in the Time Domain
58 LTI Filters in the Frequency Domain
Appendix
A Distribution Tables
- A.1 Discrete Distributions
- A.2 Continuous Distributions
B Complex Numbers
C Fourier Transforms
D Fourier Tables
Published with bookdown

Introduction to Probability

Dennis Sun

2020-08-14

Introduction to Probability

Preface