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18.05 | Spring 2014 | Undergraduate

# Introduction to Probability and Statistics

Listed in the following table are the in-class slides and post-class materials for each of the class sessions. The post-class version of the slides contains the solutions to the board problems, clicker questions, and discussion questions that were posed to the students during class. It was not always the case that the end of the planned set of slides was reached in each class, so the last slides in one deck may be repeated in the next deck.

WEEK # | SES # | IN-CLASS SLIDES | POST-CLASS SLIDES
--- | --- | --- | ---

Probability

1 | C1 | Introduction, counting and sets (PDF) | Class 1 Slides with Solutions (PDF)

C2 | Probability basics (PDF) | Class 2 Slides with Solutions (PDF)

2 | C3 | Conditional probability, Bayes’ theorem (PDF) | Class 3 Slides with Solutions (PDF)

C4 | Discrete random variables, expectation (PDF) | Class 4 Slides with Solutions (PDF)

3 | C5 | Variance, continuous random variables (PDF) Gallery of continuous variables, histograms (PDF) | Class 5 Slides with Solutions (PDF) Class 5 Slides, cont’d with Solutions (PDF)

4 | C6 | Expectation, variance, law of large numbers and central limit theorem (PDF) | Class 6 Slides with Solutions (PDF)

C7 | Joint distributions: Independence, covariance and correlation (PDF) | Class 7 Slides with Solutions (PDF)

5 | C8 | Review for exam 1 (PDF) | Class 8 Slides with Solutions (PDF)

C9 | No slides; exam 1 during class |

Statistics: Bayesian Inference

5 | C10 | Introduction to statistics; maximum likelihood estimates (PDF) | Class 10 Slides with Solutions (PDF)

6 | C11 | Bayesian updating with known discrete priors (PDF) | Class 11 Slides with Solutions (PDF)

C12 | Bayesian updating: Probabilistic prediction; odds (PDF) | Class 12 Slides with Solutions (PDF)

7 | C13 | Bayesian updating: Continuous prior, discrete data (PDF) | Class 13 Slides with Solutions (PDF)

C14 | Beta distributions: Continuous data (PDF) | Class 14 Slides with Solutions (PDF)

8 | C15 | Conjugate priors; choosing priors (PDF) | Class 15 Slides with Solutions (PDF)

C16 | Probability intervals (PDF) | Class 16 Slides with Solutions (PDF)

Statistics: Frequentist Inference—Null Hypothesis Significance Testing (NHST)

9 | C17 | Frequentist methods; NHST (PDF - 1.1MB) | Class 17 Slides with Solutions (PDF - 1.4MB)

C18 | NHST II: Significance level, power, t-tests (PDF) | Class 18 Slides with Solutions (PDF)

10 | C19 | NHST III: Gallery of tests (PDF) | Class 19 Slides with Solutions (PDF)

C20 | Comparison of Bayesian and frequentist inference (PDF) | Class 20 Slides with Solutions (PDF)

11 | C21 | Review for exam 2 (PDF) | Solutions file: Review of exam 2 (PDF)

Statistics: Confidence Intervals; Regression

12 | C22 | Confidence intervals for normal data (PDF) | Class 22 Slides with Solutions (PDF)

C23 | Confidence intervals II (PDF) | Class 23 Slides with Solutions (PDF)

13 | C24 | Bootstrap confidence intervals (PDF) | Class 24 Slides with Solutions (PDF)

C25 | Linear regression (PDF) | Class 25 Slides with Solutions (PDF)

14 | C26 | Problems file: Review for final exam (PDF) Solutions file: Review of final exam (PDF)

C27 | Problems file: Review for final exam, cont’d (PDF) Solutions file: Review of final exam, cont’d (PDF)

## 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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