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  • Chapter 1: Fundamentals
    • 1.1 Outcome Space and Events
    • 1.2 Equally Likely Outcomes
    • 1.3 Collisions in Hashing
    • 1.4 The Birthday Problem
    • 1.5 An Exponential Approximation
  • Chapter 2: Calculating Chances
    • 2.1 Addition
    • 2.2 Examples
    • 2.3 Multiplication
    • 2.4 More Examples
    • 2.5 Updating Probabilities
  • Chapter 3: Random Variables
    • 3.1 Functions on an Outcome Space
    • 3.2 Distributions
    • 3.3 Equality
  • Chapter 4: Relations Between Variables
    • 4.1 Joint Distributions
    • 4.2 Marginal Distributions
    • 4.3 Conditional Distributions
    • 4.4 Updating Distributions
    • 4.5 Dependence and Independence
  • Chapter 5: Collections of Events
    • 5.1 Bounding the Chance of a Union
    • 5.2 Inclusion-Exclusion
    • 5.3 The Matching Problem
    • 5.4 Sampling Without Replacement
  • Review Problem Set 1
  • Chapter 6: Random Counts
    • 6.1 The Binomial Distribution
    • 6.2 Examples
    • 6.3 The Hypergeometric Distribution
    • 6.4 Odds Ratios
    • 6.5 The Law of Small Numbers
  • Chapter 7: Poissonization
    • 7.1 Poissonizing the Binomial
    • 7.2 Poissonizing the Multinomial
  • Chapter 8: Expectation
    • 8.1 Definition
    • 8.2 Additivity
    • 8.3 Expectations of Functions
  • Review Problems: Set 2
  • Chapter 9: Conditioning, Revisited
    • 9.1 Probability by Conditioning
    • 9.2 Expectation by Conditioning
    • 9.3 Expected Waiting Times
  • Chapter 10: Markov Chains
    • 10.1 Transitions
    • 10.2 Deconstructing Chains
    • 10.3 Long Run Behavior
    • 10.4 Examples
  • Chapter 11: Reversing Markov Chains
    • 11.1 Detailed Balance
    • 11.2 Reversibility
    • 11.3 Code Breaking
    • 11.4 Markov Chain Monte Carlo
  • Review Set on Conditioning and Markov Chains
  • Chapter 12: Standard Deviation
    • 12.1 Definition
    • 12.2 Prediction and Estimation
    • 12.3 Tail Bounds
    • 12.4 Heavy Tails
  • Chapter 13: Variance Via Covariance
    • 13.1 Properties of Covariance
    • 13.2 Sums of IID Samples
    • 13.3 Sums of Simple Random Samples
    • 13.4 Finite Population Correction
  • Chapter 14: The Central Limit Theorem
    • 14.1 Exact Distribution
    • 14.2 PGFs in NumPy
    • 14.3 Central Limit Theorem
    • 14.4 The Sample Mean
    • 14.5 Confidence Intervals
  • Chapter 15: Continuous Distributions
    • 15.1 Density and CDF
    • 15.2 The Meaning of Density
    • 15.3 Expectation
    • 15.4 Exponential Distribution
    • 15.5 Calculus in SymPy
  • Review Problems: Set 3
  • Chapter 16: Transformations
    • 16.1 Linear Transformations
    • 16.2 Monotone Functions
    • 16.3 Two-to-One Functions
  • Chapter 17: Joint Densities
    • 17.1 Probabilities and Expectations
    • 17.2 Independence
    • 17.3 Marginal and Conditional Densities
    • 17.4 Beta Densities with Integer Parameters
  • Chapter 18: The Normal and Gamma Families
    • 18.1 Standard Normal: The Basics
    • 18.2 Sums of Independent Normal Variables
    • 18.3 The Gamma Family
    • 18.4 Chi-Squared Distributions
  • Review Problems: Set 4
  • Chapter 19: Distributions of Sums
    • 19.1 The Convolution Formula
    • 19.2 Moment Generating Functions
    • 19.3 MGFs, the Normal, and the CLT
    • 19.4 Chernoff Bound
  • Chapter 20: Approaches to Estimation
    • 20.1 Maximum Likelihood
    • 20.2 Prior and Posterior
    • 20.3 Independence, Revisited
  • Chapter 21: The Beta and the Binomial
    • 21.1 Updating and Prediction
    • 21.2 The Beta-Binomial Distribution
    • 21.3 Long Run Proportion of Heads
  • Chapter 22: Prediction
    • 22.1 Conditional Expectation As a Projection
    • 22.2 Variance by Conditioning
    • 22.3 Examples
    • 22.4 Least Squares Predictor
  • Chapter 23: Jointly Normal Random Variables
    • 23.1 Random Vectors
    • 23.2 Multivariate Normal Distribution
    • 23.3 Linear Combinations
    • 23.4 Independence
  • Chapter 24: Simple Linear Regression
    • 24.1 Bivariate Normal Distribution
    • 24.2 Least Squares Linear Predictor
    • 24.3 Regression and the Bivariate Normal
    • 24.4 The Regression Equation
  • Chapter 25: Multiple Regression
    • 25.1 Bilinearity in Matrix Notation
    • 25.2 Best Linear Predictor
    • 25.3 Conditioning and the Multivariate Normal
    • 25.4 Multiple Regression
  • Further Review Exercises

Prob 140

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  • Probability for Data Science

Probability for Data Science

By Ani Adhikari and Jim Pitman

This is the textbook for the Probability for Data Science class at UC Berkeley.

The contents of this book are licensed for free consumption under the following license:
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

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