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# Material for Midterm

The midterm is in class on Wednesday October 3. This is a summary of the material for the exam, grouped by main topic. The general techniques are in the sections Probability, Distribution, and Expectation. The next two sections consist of applications.

Labs are listed by topic. Please also review your homework, quizzes, and the problems in the Review Sets at the ends of Chapters 5, 8, and 11. The Spring 2017 midterm (modified to account for changes to content and sequence) will be posted on Piazza for additional practice.

Homework 6, due Tuesday October 2, consists of the Spring 2018 midterm.

### Probability

• Chapter 1, Lab 1: Spaces, events, basic counting, exponential approximation
• Chapter 2: Addition and multiplication rules, conditioning and Bayes’ rule
• Section 4.5: Partitioning events
• Chapter 5: Unions and intersections of several events
• Section 9.1: Probabilities by conditioning and recursion

### Distribution

• Chapter 3: Random variables, equality versus equality in distribution
• Chapter 4, Lab 2: Joint, marginals, conditionals, independence
• Section 5.4: Random permutations and symmetry

### Expectation

• Chapter 8: The main properties, including additivity, the method of indicators, and expectations of functions
• Lab 4: Tail sum formula for the expectation of a non-negative integer valued variable
• Section 9.2, 9.3: Expectation by conditioning

### Random Counts

• Section 8.1: Bernoulli
• Section 8.1: Uniform on a, a+1, … , b
• Sections 6.1, 6.2, 6.4, 7.2: Binomial and multinomial
• Sections 5.4, 6.3, Lab 2: Hypergeometric
• Section 6.5, Lab 3, Chapter 7: Poisson
• Section 9.3, Homework 4: Geometric

### Markov Chains

• Sections 10.1, 10.2: Terminology and basics
• Section 10.3, 10.4, Lab 5: The steady state distribution and its properties
• Section 11.1, 11.2: The detailed balance equations and their primary use
• Sections 11.3, Lab 6: Code breaking by MCMC

### Omitted from Midterm

• All code. You will neither have to read nor write code on the midterm, though you will on the final.
• Total variation distance: Lab 3, HW 3