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18.05 | Spring 2014 | Undergraduate

# Introduction to Probability and Statistics

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 # | SES # | TOPICS | READINGS | SLIDES | PROBLEM SETS
--- | --- | --- | --- | --- | ---
Probability
1 | C1 | Introduction, counting and sets | 1a: Introduction (PDF) 1b: Counting and Sets (PDF) | Class 1 Slides (PDF) Class 1 Slides with Solutions (PDF) | Problem Set 1 (PDF) Problem Set 1 Solutions (PDF)
C2 | Probability basics | 2: Probability: Terminology and Examples (PDF) R Tutorial 1A: Basics R Tutorial 1B: Random Numbers | Class 2 Slides (PDF) Class 2 Slides with Solutions (PDF)
S1 | Birthday matches; Introduction to R |  |
2 | C3 | Conditional probability, Bayes’ theorem | 3: Conditional Probability, Independence and Bayes’ Theorem (PDF) | Class 3 Slides (PDF) Class 3 Slides with Solutions (PDF) | Problem Set 2 (PDF) Problem Set 2 Solutions (PDF)
C4 | Discrete random variables, expectation | 4a: Discrete Random Variables (PDF) 4b: Discrete Random Variables: Expected Value (PDF) | Class 4 Slides (PDF) Class 4 Slides with Solutions (PDF)
S2 | Expectation; Simulation using R |  |
3 | C5 | Variance, continuous random variables | 5a: Variance of Discrete Random Variables (PDF) 5b: Continuous Random Variables (PDF) | Class 5 Slides (PDF) Class 5 Slides with Solutions (PDF) | Problem Set 3 (PDF) Problem Set 3 Solutions (PDF)
S3 | Gallery of continuous variables, histograms | 5c: Gallery of Continuous Random Variables (PDF) 5d: Manipulating Continuous Random Variables (PDF) | Class 5 Slides, cont’d (PDF) Class 5 Slides, cont’d with Solutions (PDF)
4 | C6 | Expectation, variance, law of large numbers and central limit theorem | 6a: Expectation, Variance and Standard Deviation for Continuous Random Variables (PDF) 6b: Central Limit Theorem and the Law of Large Numbers (PDF) 6c: Appendix (PDF) | Class 6 Slides (PDF) Class 6 Slides with Solutions (PDF) | Problem Set 4 (PDF) Problem Set 4 Solutions (PDF)
C7 | Joint distributions: independence, covariance and correlation | 7a: Joint Distributions, Independence (PDF) 7b: Covariance and Correlation (PDF) | Class 7 Slides (PDF) Class 7 Slides with Solutions (PDF)
S4 | Covariance, correlation, CLT |  |
5 | C8 | Review for exam 1 | Class 8: Exam Review (PDF) Class 8: Exam Review Solutions (PDF) | Class 8 Slides (PDF) Class 8 Slides with Solutions (PDF) |
C9 | Exam 1 |  |  |
Statistics: Bayesian Inference
5 | C10 | Introduction to statistics; maximum likelihood estimates | 10a: Introduction to Statistics (PDF) 10b: Maximum Likelihood Estimates (PDF) | Class 10 Slides (PDF) Class 10 Slides with Solutions (PDF) |
6 | C11 | Bayesian updating with known discrete priors | 11: Bayesian Updating with Discrete Priors (PDF) | Class 11 Slides (PDF) Class 11 Slides with Solutions (PDF) | Problem Set 5 (PDF) Problem Set 5 Solutions (PDF)
C12 | Bayesian updating: probabilistic prediction; odds | 12a: Bayesian Updating: Probabilistic Prediction (PDF) 12b: Bayesian Updating: Odds (PDF) | Class 12 Slides (PDF) Class 12 Slides with Solutions (PDF)
S5 | Bayesian updating |  |
7 | C13 | Bayesian updating: continuous prior, discrete data | 13a: Bayesian Updating with Continuous Priors (PDF) 13b: Notational Conventions (PDF) | Class 13 Slides (PDF) Class 13 Slides with Solutions (PDF) |
C14 | Beta distributions: continuous data | 14a: Beta Distributions (PDF) 14b: Continuous Data with continuous Priors (PDF) | Class 14 Slides (PDF) Class 14 Slides with Solutions (PDF)
S6 | Continuous data, continuous priors |  |
8 | C15 | Conjugate priors; choosing priors | 15a: Conjugate Priors: Beta and Normal (PDF) 15b: Choosing Priors (PDF) | Class 15 Slides (PDF) Class 15 Slides with Solutions (PDF) | Problem Set 6 (PDF) Problem Set 6 Solutions (PDF) Problem Set 6 R Code (R)
C16 | Probability intervals | 16: Probability Intervals (PDF) | Class 16 Slides (PDF) Class 16 Slides with Solutions (PDF)
S7 | No studio |  |
Statistics: Frequentist Inference—Null Hypothesis Significance Testing (NHST)
9 | C17 | Frequentist methods; NHST | 17a: The Frequentist School of Statistics (PDF) 17b: Null Hypothesis Significance Testing I (PDF) | Class 17 Slides (PDF) Class 17 Slides with Solutions (PDF) | Problem Set 7 (PDF) Problem Set 7 Solutions (PDF)
C18 | NHST II: Significance level, power, t-tests | 18: Null Hypothesis Significance Testing II (PDF) | Class 18 Slides (PDF) Class 18 Slides with Solutions (PDF)
S8 | Rejection regions; NHST |  |
10 | C19 | NHST III: Gallery of tests | 19: Null Hypothesis Significance Testing III (PDF) | Class 19 Slides (PDF) Class 19 Slides with Solutions (PDF) | Problem Set 8 (PDF) Problem Set 8 Solutions (PDF)
C20 | Comparison of Bayesian and frequentist inference | 20: Comparison of Frequentist and Bayesian Inference (PDF) | Class 20 Slides (PDF) Class 20 Slides with Solutions (PDF)
S9 | NHST; comparing frequentist and Bayesian methods |  |
11 | C21 | Review for exam 2 |  | Class 21 Slides (PDF) Class 21 Solutions File (PDF) |
S10 | Exam 2 |  |
Statistics: Confidence Intervals; Regression
12 | C22 | Confidence intervals for normal data | 22: Confidence Intervals Based on Normal Data (PDF) | Class 22 Slides (PDF) Class 22 Slides with Solutions (PDF) | Problem Set 9 (PDF) Problem Set 9 Solutions (PDF)
C23 | Confidence intervals II | 23a: Confidence Intervals: Three Views (PDF) 23b: Confidence Intervals for the Mean of Non-normal Data (PDF) | Class 23 Slides (PDF) Class 23 Slides with Solutions (PDF)
S11 | Confidence intervals III |  |
13 | C24 | Bootstrap confidence intervals | 24: Bootstrap Confidence Intervals (PDF) | Class 24 Slides (PDF) Class 24 Slides with Solutions (PDF) |
C25 | Linear regression | 25: Linear Regression (PDF) | Class 25 Slides (PDF) Class 25 Slides with Solutions (PDF)
S12 | Bootstrapping; linear regression |  |
14 | C26 | Review for final exam |  | Class 26 Slides (PDF) Class 26 Problems File (PDF) Class 26 Solutions File (PDF) |
C27 | Review for final exam, cont’d |  | Class 27 Slides (PDF) Class 27 Problems File (PDF) Class 27 Solutions File (PDF)
15 |  | Final exam |  |  |

## Course Info

##### Instructors

- Dr. Jeremy Orloff
- Jonathan Bloom

##### Departments

- Mathematics

##### As Taught In

Spring 2014

##### Level

Undergraduate

##### Topics

- Mathematics
  - Discrete Mathematics
  - Probability and Statistics

##### Learning Resource Types

assignment_turned_in Problem Sets with Solutions
grading Exams with Solutions
notes Lecture Notes
co_present Instructor Insights
theaters Other Video

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