# Material for the Midterm

### Prob 140 Spring 2019

The midterm will be during the lecture hour (5:10 p.m. to 6:30 p.m.) on Thursday 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.

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.

Homework 5, due Tuesday February 26, consists of the Fall 2018 midterm. The Spring 2018 midterm will be posted for additional practice.

### Finding Probabilities

• Chapter 1, Lab 1: Spaces, events, basic counting, exponential approximation
• Chapter 2: Addition and multiplication rules, conditioning and Bayes’ rule
• Section 4.2: 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: Joint, marginals, conditionals, independence
• Section 5.4: Random permutations and symmetry
• Chapter 7, Lab 3: Cdf and tails

### Expectation

• Chapter 8: Balance point of histogram; additivity, the method of indicators, expectations of functions (linear and non-linear); unbiased estimates
• Lab 3, Homework 3: Tail sum formula for the expectation of a non-negative integer valued variable
• Section 9.2, 9.3, Lab 4: 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: Hypergeometric
• Section 6.5, Lab 2, Chapter 7: Poisson and approximately Poisson
• Section 9.3, Homework 3, Lab 4: Geometric and approximately shifted 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 5: 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.
• The derivation of the interpretation of total variation distance as the largest difference of probabilities (Homework 2)