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- file: content/README
title: Authors and License
- part: Introduction
chapters:
- url: http://prob140.org
title: Course Home
- file: content/To_the_Student
- part: Chapters
numbered: true
chapters:
- file: content/Chapter_01/00_Fundamentals
expand_sections: true
sections:
- file: content/Chapter_01/01_Outcome_Space_and_Events
- file: content/Chapter_01/02_Equally_Likely_Outcomes
- file: content/Chapter_01/03_Collisions_in_Hashing
- file: content/Chapter_01/04_Birthday_Problem
- file: content/Chapter_01/05_An_Exponential_Approximation
- file: content/Chapter_01/06_Exercises
- file: content/Chapter_02/00_Calculating_Chances
expand_sections: true
sections:
- file: content/Chapter_02/01_Addition
- file: content/Chapter_02/02_Examples
- file: content/Chapter_02/03_Multiplication
- file: content/Chapter_02/04_More_Examples
- file: content/Chapter_02/05_Updating_Probabilities
- file: content/Chapter_02/06_Exercises
- file: content/Chapter_03/00_Random_Variables
expand_sections: true
sections:
- file: content/Chapter_03/01_Functions_on_an_Outcome_Space
- file: content/Chapter_03/02_Distributions
- file: content/Chapter_03/03_Equality
- file: content/Chapter_03/04_Exercises
- file: content/Chapter_04/00_Relations_Between_Variables
expand_sections: true
sections:
- file: content/Chapter_04/01_Joint_Distributions
- file: content/Chapter_04/02_Examples
- file: content/Chapter_04/03_Marginal_Distributions
- file: content/Chapter_04/04_Conditional_Distributions
- file: content/Chapter_04/05_Dependence_and_Independence
- file: content/Chapter_04/06_Exercises
- file: content/Chapter_05/00_Collections_of_Events
expand_sections: true
sections:
- file: content/Chapter_05/01_Bounding_the_Chance_of_a_Union
- file: content/Chapter_05/02_Inclusion_Exclusion
- file: content/Chapter_05/03_The_Matching_Problem
- file: content/Chapter_05/04_Sampling_Without_Replacement
- file: content/Chapter_05/05_Exercises
- file: content/Chapter_06/00_Random_Counts
expand_sections: true
sections:
- file: content/Chapter_06/01_Binomial_Distribution
- file: content/Chapter_06/02_Examples
- file: content/Chapter_06/03_Multinomial_Distribution
- file: content/Chapter_06/04_The_Hypergeometric_Revisited
- file: content/Chapter_06/05_Odds_Ratios
- file: content/Chapter_06/06_Law_of_Small_Numbers
- file: content/Chapter_06/07_Exercises
- file: content/Chapter_07/00_Poissonization
expand_sections: true
sections:
- file: content/Chapter_07/01_Poisson_Distribution
- file: content/Chapter_07/02_Poissonizing_the_Binomial
- file: content/Chapter_07/03_Poissonizing_the_Multinomial
- file: content/Chapter_07/04_Exercises
- file: content/Chapter_08/00_Expectation
expand_sections: true
sections:
- file: content/Chapter_08/01_Definition
- file: content/Chapter_08/02_Applying_the_Definition
- file: content/Chapter_08/03_Expectations_of_Functions
- file: content/Chapter_08/04_Additivity
- file: content/Chapter_08/05_Method_of_Indicators
- file: content/Chapter_08/06_Exercises
- file: content/Chapter_09/00_Conditioning_Revisited
expand_sections: true
sections:
- file: content/Chapter_09/01_Probability_by_Conditioning
- file: content/Chapter_09/02_Expectation_by_Conditioning
- file: content/Chapter_09/03_Expected_Waiting_Times
- file: content/Chapter_09/04_Exercises
- file: content/Chapter_10/00_Markov_Chains
expand_sections: true
sections:
- file: content/Chapter_10/01_Transitions
- file: content/Chapter_10/02_Deconstructing_Chains
- file: content/Chapter_10/03_Long_Run_Behavior
- file: content/Chapter_10/04_Examples
- file: content/Chapter_11/00_Markov_Chain_Monte_Carlo
expand_sections: true
sections:
- file: content/Chapter_11/01_Balance_and_Detailed_Balance
- file: content/Chapter_11/02_Code_Breaking
- file: content/Chapter_11/03_Metropolis_Algorithm
- file: content/Chapter_11/04_Exercises
- file: content/Chapter_12/00_Standard_Deviation
expand_sections: true
sections:
- file: content/Chapter_12/01_Definition
- file: content/Chapter_12/02_Prediction_and_Estimation
- file: content/Chapter_12/03_Bounds
- file: content/Chapter_12/04_Heavy_Tails
- file: content/Chapter_12/05_Exercises
- file: content/Chapter_13/00_Variance_Via_Covariance
expand_sections: true
sections:
- file: content/Chapter_13/01_Covariance
- file: content/Chapter_13/02_Properties_of_Covariance
- file: content/Chapter_13/03_Sums_of_Independent_Variables
- file: content/Chapter_13/04_Symmetry_and_Indicators
- file: content/Chapter_13/05_Finite_Population_Correction
- file: content/Chapter_13/06_Exercises
- file: content/Chapter_14/00_The_Central_Limit_Theorem
expand_sections: true
sections:
- file: content/Chapter_14/01_Exact_Distribution_of_a_Sum
- file: content/Chapter_14/02_PGFs_in_NumPy
- file: content/Chapter_14/03_Central_Limit_Theorem
- file: content/Chapter_14/04_SciPy_and_Normal_Curves
- file: content/Chapter_14/05_The_Sample_Mean
- file: content/Chapter_14/06_Confidence_Intervals
- file: content/Chapter_14/07_Exercises
- file: content/Chapter_15/00_Continuous_Distributions
expand_sections: true
sections:
- file: content/Chapter_15/01_Density_and_CDF
- file: content/Chapter_15/02_The_Meaning_of_Density
- file: content/Chapter_15/03_Expectation
- file: content/Chapter_15/04_Exponential_Distribution
- file: content/Chapter_15/05_Calculus_in_SymPy
- file: content/Chapter_15/06_Exercises
- file: content/Chapter_16/00_Transformations
expand_sections: true
sections:
- file: content/Chapter_16/01_Linear_Transformations
- file: content/Chapter_16/02_Monotone_Functions
- file: content/Chapter_16/03_Simulation_via_the_CDF
- file: content/Chapter_16/04_Two_to_One_Functions
- file: content/Chapter_16/05_Exercises
- file: content/Chapter_17/00_Joint_Densities
expand_sections: true
sections:
- file: content/Chapter_17/01_Probabilities_and_Expectations
- file: content/Chapter_17/02_Independence
- file: content/Chapter_17/03_Marginal_and_Conditional_Densities
- file: content/Chapter_17/04_Beta_Densities_with_Integer_Parameters
- file: content/Chapter_17/05_Exercises
- file: content/Chapter_18/00_The_Normal_and_Gamma_Families
expand_sections: true
sections:
- file: content/Chapter_18/01_Standard_Normal_Basics
- file: content/Chapter_18/02_Sums_of_Independent_Normal_Variables
- file: content/Chapter_18/03_The_Gamma_Family
- file: content/Chapter_18/04_Chi_Squared_Distributions
- file: content/Chapter_18/05_Exercises
- file: content/Chapter_19/00_Distributions_of_Sums
expand_sections: true
sections:
- file: content/Chapter_19/01_Convolution_Formula
- file: content/Chapter_19/02_Moment_Generating_Functions
- file: content/Chapter_19/03_MGFs_Normal_and_the_CLT
- file: content/Chapter_19/04_Chernoff_Bound
- file: content/Chapter_19/05_Exercises
- file: content/Chapter_20/00_Approaches_to_Estimation
expand_sections: true
sections:
- file: content/Chapter_20/01_Maximum_Likelihood
- file: content/Chapter_20/02_Independence_Revisited
- file: content/Chapter_20/03_Prior_and_Posterior
- file: content/Chapter_20/04_Exercises
- file: content/Chapter_21/00_The_Beta_and_the_Binomial
expand_sections: true
sections:
- file: content/Chapter_21/01_Updating_and_Prediction
- file: content/Chapter_21/02_Beta_Binomial_Distribution
- file: content/Chapter_21/03_Long_Run_Proportion_of_Heads
- file: content/Chapter_21/04_Exercises
- file: content/Chapter_22/00_Prediction
expand_sections: true
sections:
- file: content/Chapter_22/01_Conditional_Expectation_Projection
- file: content/Chapter_22/02_Least_Squares_Predictor
- file: content/Chapter_22/03_Variance_by_Conditioning
- file: content/Chapter_22/04_Examples
- file: content/Chapter_22/05_Exercises
- file: content/Chapter_23/00_Multivariate_Normal_RVs
expand_sections: true
sections:
- file: content/Chapter_23/01_Random_Vectors
- file: content/Chapter_23/02_Multivariate_Normal_Distribution
- file: content/Chapter_23/03_Linear_Combinations
- file: content/Chapter_23/04_Independence
- file: content/Chapter_23/05_Exercises
- file: content/Chapter_24/00_Simple_Linear_Regression
expand_sections: true
sections:
- file: content/Chapter_24/01_Linear_Least_Squares
- file: content/Chapter_24/02_Bivariate_Normal_Distribution
- file: content/Chapter_24/03_Regression_and_Bivariate_Normal
- file: content/Chapter_24/04_Regression_Equation
- file: content/Chapter_24/05_Exercises
- file: content/Chapter_25/00_Multiple_Regression
expand_sections: true
sections:
- file: content/Chapter_25/01_Bilinearity_in_Matrix_Notation
- file: content/Chapter_25/02_Best_Linear_Predictor
- file: content/Chapter_25/03_Multivariate_Normal_Conditioning
- file: content/Chapter_25/04_Multiple_Regression
# - file: content/Chapter_25/05_Further_Review_Exercises
# - file: content/introduction/notebooks