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# Material for the Midterm

### Prob140 Fall 2019

The midterm is during the lecture time on Thursday October 10. 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 October 8, consists of last semester’s midterm.

### 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 8: The main properties, including additivity, the method of indicators, and expectations of functions, and tail sum formula for the expectation of a non-negative integer valued variable
• Lab 3: Application of tail sum formula
• Sections 9.2, 9.3: Expectation by conditioning
• Lab 4: Waiting times till patterns: application of 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 1: Hypergeometric
• Section 6.5, Chapter 7: Poisson
• Sections 8.1, 9.3: Geometric

### Markov Chains

• Sections 10.1, 10.2: Terminology and basics
• Sections 10.3, 10.4: The steady state distribution and its properties
• Section 11.1, 11.2: Detailed balance
• Sections 11.3, 11.4: Code Breaking and MCMC