Material for Midterm 1

Data 140 Spring 2026

A. Adhikari

Material for Midterm 1

Midterm 1 is on Wednesday 2/18 from 7:10 PM to 8:40 PM. The scope is Chapters 1 through 8.

Here is a summary of the material for the exam, grouped by main topic. Boldface has been reserved for topics that we consider to be core material for understanding the rest of the course.

The general techniques are in the sections Probability, Distribution, and Expectation. The Random Counts section consists of applications.

In several chapters, the book has sections called Examples. Please review those. Please also review all your homework, labs (the mathematical parts; see the list at the end of this doc), and exercises done in section.

You will not have to write code on the midterm. Any code that you may have to read will be straightforward with comments that explain exactly what it is doing.

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

Distribution

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

Expectation

Chapter 8: The main properties, including additivity, the method of indicators, and expectations of functions (linear and non-linear), as well as the tail sum formula for the expectation of a non-negative integer valued variable

Random Counts

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

Section 8.1: Bernoulli
Section 8.2: Uniform on a, a+1, … , b
Sections 6.1, 6.3, 6.5, 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: Poisson and related expectations
Poisson-binomial: Lab 3 Section 5
Section 8.2: Geometric, its right hand tail, and its expectation

Lab Sections in Scope

Lab 1: Start by reviewing the birthday problem and the related exponential approximation. Then study 2a, the approximation in 3a, and the derivation of the distribution in 4a-c.
Lab 2: The formula for the TVD is at the top of Section 1, but the key is 1b. Look carefully at the Poisson histogram in 2c, especially the modes; then study 3c for matching problem approximations. For binomial approximations, study 4a, 4c.
Lab 3: First study the assumptions of the process, under The Process above Part A. See what happens as \(\theta\) changes; look at 2d as well. Then study 1c, 4a, 4c, 5a, 5b.