Introduction to Probability and Statistics

Classes: Reading and In-class Materials

Note to OCW Users: The online reading questions below are available on MIT’s Open Learning Library, which is free to use. You have the option to enroll to track your progress, or you can view and use the materials without enrolling. The MITx/18.05r content mentioned in this course site are linked to the Open Learning Library.

For the assigned readings below students were expected to complete prior to attending class sessions. Students also completed online multiple choice or numerical answer questions based on each week’s readings. Students received instant feedback and could make multiple attempts.

Some of the classes use R code and R studios. You can find these materials from R: Information, Tutorials, and Sample Code page.

All Probability Readings in One (PDF)   

All Statistics Readings in One (PDF)     

Unit 1: Probability

Class 1      

• Class 1a Reading: Introduction (PDF)             
• Class 1b Reading: Counting and Sets (PDF)   
• Class 1 online reading questions 
• Class 1 Slides: Introduction, Counting, and Sets (PDF)
  • Class 1 In-class Problems (PDF)
  • Class 1 In-class Problem Solutions (PDF)        

Class 2

• Class 2 Reading: Probability: Terminology and Examples (PDF)         
• R Tutorial A: Basics        
• R Tutorial B: Random Numbers 
• Class 2 online reading questions
• Class 2 Slides: Probability Basics  (PDF)
  • Class 2 In-class Problems (PDF)
  • Class 2 In-class Problem Solutions (PDF)

Studio 1

• Studio 1 Slides: Birthday Matches  (PDF)

 Class 3 

• Class 3 Reading: Conditional Probability, Independence, Bayes’ Theorem (PDF) 
• Class 3 online reading questions  
• Class 3 Slides: Conditional Probability, Independence, and Bayes’ Theorem (PDF)
  • Class 3 In-class Problems (PDF)
  • Class 3 In-class Problem Solutions (PDF)

 Class 4           

• Class 4a Reading: Discrete Random Variables (PDF)             
• Class 4b Reading: Expected Value of Discrete Random Variables (PDF) 
• Class 4 online reading questions about R
• Class 4 online reading questions: 1
• Class 4 online reading questions: 2
• Class 4 Slides: Discrete Random Variables: Expected Value (PDF)
  • Class 4 In-class Problems (PDF)
  • Class 4 In-class Problem Solutions (PDF)

 Class 5         

• Class 5a Reading: Variance of Discrete Random Variables (PDF)             
• Class 5b Reading: Continuous Random Variables (PDF)             
• Class 5c Reading: Gallery of Continuous Random Variables (PDF)             
• Class 5d Reading: Manipulating Random Variables (PDF)      
• Class 5 online reading questions: 1
• Class 5 online reading questions: 2
• Class 5 online reading questions: 3
• Class 5 online reading questions: 4
• Class 5a Slides: Variance of Discrete Variables; Continuous Random Variables (PDF)
  • Class 5a In-class Problems (PDF)
  • Class 5a In-class Problem Solutions (PDF)
• Class 5b Slides: Continuous Random Variables (continued) (PDF)
  • Class 5b In-class Problems (PDF)
  • Class 5b In-class Problem Solutions (PDF)

 Class 6      

• Class 6a Reading: Continuous Random Variables: Expectation and Variance (PDF)             
• Class 6b Reading: Central Limit Theorem (PDF)             
• Class 6c Reading: Appendix (PDF) 
• Class 6 online reading questions about variance
• Class 6 online reading questions about central limit theorem and law of large numbers
• Class 6a Slides: Continuous Random Variables: Expected Value and Variance; Histograms (PDF)
  • Class 6a In-class Problems (PDF)
  • Class 6a In-class Problem Solutions (PDF)
• Class 6b Slides: Law of Large Numbers, Central Limit Theorem, Histograms (PDF)
  • Class 6b In-class Problems (PDF)
  • Class 6b In-class Problem Solutions (PDF)

 Class 7       

• Class 7a Reading: Joint Distributions, Independence (PDF)             
• Class 7b Reading: Covariance and Correlation (PDF)      
• Class 7 online reading questions about joint distributions
• Class 7 online reading questions about covariance and correlation
• Class 7 Slides: Joint Distributions: Independence, Covariance, and Correlation (PDF)
  • Class 7 In-class Problems (PDF)
  • Class 7 In-class Problem Solutions (PDF)

Class 8

• Class 8 Slides: Review for Exam 1 (PDF)
• Normal Probability Table (PDF)
• Exam 1 Review List (PDF)
  • Class 8 In-class Problems (PDF)
  • Class 8 In-class Problem Solutions (PDF)

Unit 2: Statistics: Bayesian Inference      

 Class 10    

• Class 10a Reading: Introduction to Statistics (PDF)             
• Class 10b Reading: Maximum Likelihood Estimates (PDF) 
• Class 10 online reading questions about introduction to statistics
• Class 10 online reading questions about maximum likelihood estimate  
• Class 10 Slides: Introduction to Statistics, Examples, Likelihood, MLE (PDF)
  • Class 10 In-class Problems (PDF)
  • Class 10 In-class Problem Solutions (PDF)

 Class 11           

• Class 11 Reading: Bayesian Updating with Discrete Priors (PDF)  
• Class 11 online reading questions 
• Class 11 Slides: Bayesian Updating: Discrete Priors (PDF)
  • Class 11 In-class Problems (PDF)
  • Class 11 In-class Problem Solutions (PDF)

 Class 12            

• Class 12a Reading: Bayesian Updating: Probabilistic Prediction (PDF)             
• Class 12b Reading: Bayesian Updating: Odds (PDF)
• Class 12 online reading questions about probabilistic prediction
• Class 12 online reading questions about odds 
• Class 12 Slides: Predictive Probabilities, Bayesian Updating: Odds (PDF)
  • Class 12 In-class Problems (PDF)
  • Class 12 In-class Problem Solutions (PDF)    

 Class 13        

• Class 13a Reading: Bayesian Updating with Continuous Priors (PDF)             
• Class 13b Reading: Notational Conventions (PDF)  
• Class 13 online reading questions 
• Class 13 Slides: Bayesian Updating: Continuous Prior, Discrete Data (PDF)
  • Class 13 In-class Problems (PDF)
  • Class 13 In-class Problem Solutions (PDF)  

 Class 14     

• Class 14 Reading: Continuous Data with Continuous Priors (PDF) (optional)  

 Class 15          

• Class 15 Reading: Beta Distributions, Conjugate Priors: Beta and Normal (PDF)   
• Class 15 online reading questions about conjugate priors and beta
• Class 15 online reading questions about conjugate priors and choosing priors
• Class 15 Slides: Beta Distributions, Conjugate Priors; Choosing Priors (PDF)
  • Class 15 In-class Problems (PDF)
  • Class 15 In-class Problem Solutions (PDF)

 Class 16           

• Class 16a Reading: Choosing Priors (PDF)             
• Class 16b Reading: Probability Intervals (PDF) 
• Class 16 online reading questions 
• Class 16 Slides: Choosing Priors; Probability Intervals (PDF)
  • Class 16 In-class Problems (PDF)
  • Class 16 In-class Problem Solutions (PDF)  

Unit 3 Statistics: Frequentist Inference: NHST       

 Class 17  

• Class 17a Reading: The Frequentist School of Statistics (PDF)             
• Class 17b Reading: NHST I (PDF) 
• Class 17 online reading questions 
• Class 17 Slides: The Frequentist School of Statistics; NHST I (PDF)
  • Class 17 In-class Problems (PDF)
  • Class 17 In-class Problem Solutions (PDF) 

 Class 18            

• Class 18 Reading: NHST II (PDF) 
• Class 18 online reading questions
• Class 18 Slides: NHST II (PDF)
  • Class 18 In-class Problems (PDF)
  • Class 18 In-class Problem Solutions (PDF)

 Class 19              

• Class 19 Reading: NHST III (PDF)
• Class 19 online reading questions 
• Class 19 Slides: NHST III (PDF)
  • Class 19 In-class Problems (PDF)
  • Class 19 In-class Problem Solutions (PDF)  

 Class 20            

• Class 20 Reading: Comparison of Frequentist and Bayesian Inference (PDF)  
• Class 20 online reading questions 
• Class 20 Slides: Comparison of Bayes and NHST (PDF)
  • Class 20 In-class Problems (PDF)
  • Class 20 In-class Problem Solutions (PDF)

Class 21

• Class 21 Slides: Review for Exam 2 (PDF)
• Summary of NHST (PDF)
• Probability Table (PDF)
  • Class 21 In-class Problems (PDF)
  • Class 21 In-class Problem Solutions (PDF)

Unit 4 Statistics: Confidence Intervals; Regression       

Class 22

• Class 22 Reading: Confidence Intervals Based on Normal Data (PDF)   
• Class 22 online reading questions 
• Class 22 Slides: Confidence Intervals (PDF)
  • Class 22 In-class Problems (PDF)
  • Class 22 In-class Problem Solutions (PDF) 

Class 23        

• Class 23a Reading: Confidence Intervals: Three Views (PDF)             
• Class 23b Reading: Confidence Intervals for the Mean of Non-normal Data (PDF) 
• Class 23 online reading questions
• Class 23 Slides: Confidence Intervals (continued) (PDF)
  • Class 23 In-class Problems (PDF)
  • Class 23 In-class Problem Solutions (PDF)    

Class 24        

• Class 24 Reading: Bootstrap Confidence Intervals (PDF)
• Class 24 online reading questions
• Class 24 Slides: Bootstrap Confidence Intervals (PDF)
  • Class 24 In-class Problems (PDF)
  • Class 24 In-class Problem Solutions (PDF)   

Class 26          

• Class 26 Reading: Linear Regression (PDF)
• Class 26 online reading questions
• Class 26 Slides: Linear and Multiple Regression (PDF)
  • Class 26 In-class Problems (PDF)
  • Class 26 In-class Problem Solutions (PDF)

Class 27

• Class 27: Review for Final Exam (no slides)
  • Class 27 In-class Problems (PDF)
  • Class 27 In-class Problem Solutions (PDF)