Probability

I. Introduction

Probability is the math of uncertainty. It gives you a way to model random events, measure risk, and predict long-run behavior.

II. Outline

• Probability I — Foundations & Counting
  • Sample spaces, events, set operations
  • Axioms of probability, complements, unions/intersections
  • Counting: permutations, combinations, inclusion–exclusion
  • Common discrete models
• Probability II — Conditional Probability & Bayes
  • Conditional probability and independence
  • Law of Total Probability
  • Bayes’ Rule
• Probability III — Random Variables & Distributions
  • Discrete vs continuous random variables
  • PMF / PDF / CDF
  • Expectation, variance, covariance, correlation
  • Common distributions:
    • Discrete: Bernoulli, Binomial, Geometric, Negative Binomial, Poisson
    • Continuous: Uniform, Exponential, Normal, Gamma, Beta
  • Joint distributions, independence, conditioning on random variables
  • Transformations
• Probability IV — Long-Run Behavior & Applications
  • Law of Large Numbers
  • Central Limit Theorem
  • Approximations
  • Markov chains, Poisson process
  • Applications: reliability, queues, networks, finance risk basics

III. Free Books

• UMN Open Textbook Library - Search for Probability
  • Introduction to Probability
  • Applied Probability
  • Probability and Statistics for Programmers
• MIT OCW Textbook - Introduction to Probability
  • RES.6.041 Fall 2000
  • Probability for Data Science

IV. Video Series

Introduction to Probability:

• MIT OCW 6-012 YouTube Playlist
• Harvard Stat110 YouTube Playlist

V. See Also

Statistics, Discrete Math, Calculus, Linear Algebra