18.05 | Spring 2022 | Undergraduate

# Introduction to Probability and Statistics

## Calendar

Students are required to attend class sessions and studio sessions, the latter of which take place on Friday. Typically, studio sessions are used to introduce longer problems and the use of R.

### Week 1

#### Unit 1: Probability

• Class 1: Counting
• Class 2: Probability Basics
• Studio 1: Birthday Matches

### Week 2

Key Date: Problem set 1 due

• Class 3: Conditional Probability, Independence, and Bayes’ Theorem
• Class 4: Discrete Random Variables: Expected Value
• Studio 2: Binomial Distributions; Derangements

### Week 3

Key Date: Problem set 2 due

• Class 5a: Variance of Discrete Variables; Continuous Random Variables
• Class 5b: Continuous Random Variables (continued)
• Studio 3: Histograms

### Week 4

Key Date: Problem set 3 due

• Class 6a: Continuous Random Variables: Expected Value and Variance; Histograms
• Class 6b: Law of Large Numbers, Central Limit Theorem, Histograms

### Week 5

Key Date: Problem set 4 due

• Class 7: Joint Distributions: Independence, Covariance, and Correlation
• Class 8: Review for Exam 1
• Studio 4: Covariance and Correlation

### Week 6

Key Date: Problem set 5 due

• Class 9: Exam 1

#### Unit 2 Statistics: Bayesian Inference

• Class 10: Introduction to Statistics, Examples, Likelihood, MLE

### Week 7

Key Date: Problem set 6 due

• Class 11: Bayesian Updating: Discrete Priors
• Class 12: Predictive Probabilities, Bayesian Updating: Odds
• Studio 5: Discrete Bayesian Updating

### Week 8

• Class 13: Bayesian Updating: Continuous Prior, Discrete Data
• Class 14: Continuous Data with Continuous Priors (Optional)
• Class 15: Beta Distributions, Conjugate Priors; Choosing Priors
• Studio 6: Discretized Continuous Bayesian Updating

### Week 9

Key Date: Problem set 7 due

• Class 16: Choosing Priors; Probability Intervals

#### Unit 3 Statistics: Frequentist Inference: NHST

• Class 17: NHST: Rejection Regions, z-Test
• Studio 7: Significance Testing and the Probability of Hypotheses

### Week 10

Key Date: Problem set 8 due

• Class 18: NHST (continued) (t-Tests)
• Class 19: NHST: Distributions Related to Normal Distributions (Chi Square, ANOVA)
• Studio 8: Simulation and Computation of NHST

### Week 11

Key Date: Problem set 9 due

• Class 20: Comparison of Bayes and NHST

#### Unit 4 Statistics: Confidence Intervals; Regression

• Class 22: Confidence Intervals
• Studio 9: Simulating Confidence Intervals

### Week 12

• Class 21: Review for Exam 2
• Exam 2
• Studio 10: Bootstrap Confidence Intervals

### Week 13

Key Date: Problem set 10 due

• Class 23: Confidence Intervals (continued)
• Class 24: Bootstrap Confidence Intervals
• Class 25: R Quiz

### Week 14

Key Date: Problem set 11 due

• Class 26: Linear and Multiple Regression
• Class 27: Review for Final Exam

• Final Exam

## Course Info

Spring 2022
##### Learning Resource Types
Lecture Notes
Problem Sets with Solutions
Exams with Solutions