CS70 Guide
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  • LaTeX Reference
  • Discrete Math
    • Overview
    • Propositional Logic
    • Proofs
    • Stable Matching
    • Graphs
    • Modular Arithmetic
    • RSA Cryptography
    • Polynomials
    • Countability
    • Computability
  • Probability
    • Overview
    • Counting
    • Discrete Probability
    • Hashing and the Union Bound
    • Expectation and Variance
    • Concentration Inequalities
    • Continuous Probability
    • Markov Chains
    • The Beta Family
    • The Gamma Family
    • Conditional Expectation and Variance
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  • Probability Basics
  • Bayes' Rule
  • Random Variables
  • Probability Spaces
  • Equality

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  1. Probability

Discrete Probability

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Probability Basics

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Bayes' Rule

Bayes' Rule is used to re-express conditional probabilities P(A∣B)P(A|B)P(A∣B).

Random Variables

Probability Spaces

Probability spaces describe all of the possible values of a random variable, and how likely each of those outcomes are.

Equality

Two variables are equal if X(ω)=Y(ω)X(\omega) = Y(\omega)X(ω)=Y(ω) for all ω∈Ω\omega \in \Omegaω∈Ω, where Ω\OmegaΩ is a probability space (all possible values).

http://prob140.org/textbook/content/Chapter_03/03_Equality.html

http://prob140.org/textbook/content/Chapter_02/00_Calculating_Chances.html
Adding and subtracting probabilities
Multiplying probabilities: random draws without replacement, conditional probabilities
http://prob140.org/textbook/content/Chapter_02/05_Updating_Probabilities.html#bayes-rule
http://prob140.org/textbook/content/Chapter_02/00_Calculating_Chances.html