Material for Midterm

Data 140 Spring 2023

A. Adhikari

Material for the Midterm

The midterm is during the lecture time on Tuesday February 28. This is a summary of the material for the exam, grouped by main topic. Boldface has been reserved for topics that I consider to be core material for understanding the rest of the course.

The general techniques are in the sections Probability, Distribution, and Expectation. The next two sections consist of applications.

In several chapters, the book has sections called Examples. Please review those and all the other worked examples and Quick Checks. Please also review all your homework, labs, quizzes, and exercises done in section. If you have trouble with algebra, go over the algebra in the textbook or lectures.

Probability

• Chapter 1, Lab 1: Spaces, events, basic counting, exponential approximation
• Chapter 2: The fundamentals: addition and multiplication rules, conditioning and Bayes’ rule
• Chapter 5: Chances (or bounds on chances) of unions and intersections of several events, with major examples
• Section 9.1: Probabilities by conditioning and recursion

Distribution

• Chapter 3: Random variables, equality versus equality in distribution
• Chapter 4: Joint distribution, marginals, conditionals, independence
• Section 5.3.1 Section 5.4: Random permutations and symmetry

Expectation

• Chapter 8, Lab 3: The main properties, including additivity, the method of indicators, and expectations of functions, as well as the tail sum formula for the expectation of a non-negative integer valued variable
• Section 9.2, Section 9.3: Expectation by conditioning, applications to waiting times in i.i.d. Bernoulli trials
• Chapter 12: Expected squared error (or variance), standard deviation, and some tail bounds.

[Note: Section 12.4 is not in scope.]

Random Counts

These distributions are fundamental elements of discrete probabilitistic modeling. ALL of this section should be in bold.

• Section 8.1, 12.1.5: Bernoulli, its expectation and SD
• Section 8.1, 12.1.6: Uniform on a, a+1, … , b, its expectation and SD
• Sections 6.1, 6.3, 8.5: Binomial, multinomial, expectation of the binomial
• Sections 5.4, 6.4, 8.5: Hypergeometric and its expectation
• Section 6.6, Lab 2, Chapter 7, Sections 8.2, 8.3, 8.4, 12.1.7: Poisson, its expectation and SD
• Sections 8.2, 9.3: Geometric, its right hand tail, and its expectation

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: Balance and detailed balance
• Sections 11.2, 11.3, Lab 4: Code Breaking and MCMC