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# Material for Midterm

The midterm is in class on Wednesday February 28. 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.

The labs relevant to the midterm are listed below by topic. Please also review all your homework, quizzes, and all the practice problems in the weekly Prep Guides.

Homework 6, due Tuesday February 2/27, will consist of last year’s midterm apart from a few modifications due to changes made this year.

### Probability

• Chapter 1: Spaces, events, basic counting, exponential approximation
• Chapter 2: Addition and multiplication rules, conditioning and Bayes’ rule
• 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: Joint, marginals, conditionals, independence
• Section 5.4: Random permutations and symmetry

### Expectation

• Chapter 9: 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, 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: The detailed balance equations and their primary use

### Omitted from Midterm

• Sections 11.2, 11.3, 11.4