Neil E. Cotter

Associate Professor (Lecturer)

Electrical and Computer Engineering Dept

University of Utah

Last Updated: 10/28/20

(† = missing, * = article)

Probability

Applications | (pdf)

Probability notation compared | (pdf)

Probability Functions

Discrete (pdf)

Continuous (pdf)

Basic probability

Notation and definitions | (pdf)

Outcome

Sample space

P() ≡ probability

Event

Complement

Intersection

Mutually exclusive

Union

Partition | (pdf)

Axioms | (pdf)

Prob ≥ 0

Tot prob = 1

Example 1 (pdf)

Example 2 (pdf)

Venn diagrams | (pdf)

Example 1 | (pdf)

Example 2 | (pdf)

Example 3 | (pdf)

Law of total probability | (pdf)

Example 1 | (pdf)

Counting

Lists

Example 1 | (pdf)

Example 2 | (pdf)

Trees

Example 1 | (pdf)

Example 2 | (pdf)

Axes

Example 1 | (pdf)

Paths

†Example 1 | (pdf)

Unified approach (pdf)

Combinatorics

5-Card Game

5-card Game | (pdf) | (docx)

5-card Game Dealer (xlsx)

†Permutations (pdf)

†Combinations (pdf)

Matlab dice program

Example 1 | (pdf)

Example 2 | (pdf)

Example 3 | (pdf)

Example 4 | (pdf)

Example 5 | (pdf)

Example 6 | (pdf)

Example 7 | (pdf)

Example 8 (pdf)

Example 9 (pdf)

Example 10 (pdf)

Example 11 (pdf)

Example 12 (pdf)

Example 13 (pdf)

Example 14 | (pdf)

Example 15 | (pdf)

Binomial distribution/Bernoulli trials

Definitions | (pdf)

Binomial distribution approx | (pdf)

Binomial coefficients in polynomials | (pdf)

†Example 1 | (pdf)

Example 2 | (pdf)

Example 3 | (pdf)

Example 4 | (pdf)

Conditional probability discrete RV's

Definitions and Formulas (pdf)

Tutorial (pdf)

Discrete random variables

Example 1 (pdf)

Example 2 (pdf)

Example 3 (pdf)

Example 4 (pdf)

Spy Game (pdf)

example 1 | (pdf)

example 2 | (pdf)

example 3 | (pdf)

Probability tree (pdf)

Independent discrete RV

Definition | (pdf)

Example 1 | (pdf)

Example 2 | (pdf)

Bayes' Theorem

Tutorial (pdf)

Example 1 | (pdf)

Example 2 | (pdf)

Example 3 (pdf)

Example 4 (pdf)

Continuous random variables

†Definition | (pdf)

†d funcs for discrete distributions | (pdf)

Cumulative distribution function, F(x)

†Discrete random variables

Continuous random variables

Example 1 | (pdf)

Example 2 | (pdf)

Probability density functions, f(x)

Gallery of prob density funcs | (pdf)

Example 1 | (pdf)

Uniform distribution | (pdf)

Lognormal distribution

Example 1 | (pdf)

Example 2 | (pdf)

Chi-squared distribution

χ2 derivation | (pdf)

Example 1 | (pdf)

Example 2 | (pdf)

Normal/gaussian distribution

Table: Cumulative Normal Distribution | (pdf)

1-dimensional gaussian

Example 1 | (pdf)

2-dimensional gaussian

Mesh Plot | (pdf)

Contour Plot | (pdf)

Matlab® 2-D gaussian plot script

Matlab® 2-D gaussian plot function

Example 1 | (pdf)

Example 2 | (pdf)

N-Dimensional

†Tutorial (pdf)

†Example 1 | (pdf)

Mean/expected value

Example 1 | (pdf)

Example 2 | (pdf)

Mean = center of mass | (pdf)

†Example 1 (pdf)

Variance/standard deviation

†Example 1 (pdf)

Linear functions of rand vars | (pdf)

Example 1 | (pdf)

Example 2 | (pdf)

Nonlinear functions of rand vars

Example 1 | (pdf)

†Example 2 | (pdf)

Example 3 | (pdf)

Chebyshev's theorem

Proof (pdf) | (pdf)

Example 1 | (pdf)

Central limit theorem

Example 1 | (pdf)

Joint probability density functions, f(x, y)

Example 1 | (pdf)

Example 2 | (pdf)

Marginal probability density functions

†fX(x)

†fY(y)

Example 1 | (pdf)

Example 2 | (pdf)

Example 3 | (pdf)

Conditional probability continous RV's

†f(x | Y = y)

†f(y | X = x)

Continuous random variables

Example 1 | (pdf)

Example 2 | (pdf)

Example 3 | (pdf)

Independent Continuous random Variables

Example 1 (pdf)

Example 2 (pdf)

Example 3 (pdf)

Example 4 (pdf)

Covariance

†Example 1 | (pdf)

†Example 2 | (pdf)

†Example 3 | (pdf)

Example 4 | (pdf)

Example 5 | (pdf)

Correlation

†Example 1 | (pdf)

†Example 2 | (pdf)

†Example 3 | (pdf)

Example 4 | (pdf)

Example 5 | (pdf) | Matlab® code

†Example 6 | (pdf)

Linear combinations of rand vars

Mean value formulas | (pdf)

Variance formulas | (pdf)

Normal/gaussian distributions

Example 1 | (pdf)

Example 2 | (pdf)

Example 3 | (pdf)

Example 4 | (pdf)

Products of rand vars

Mean, Variance Formulas | (pdf)

Example 1 | (pdf)

Designing density functions

†Example 1 | (pdf)

Example 2 | (pdf)