# Material for Midterm 1

#### A. Adhikari

### Data 140 Fall 2024

# Material for Midterm 1

Midterm 1 is on Monday 9/30 from 8:10 PM to 9:40 PM. This 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), and exercises done in section.

There will be no code on the midterm. There will also be no reference sheets.

### Probability

- Chapter 1, Lab 1: Spaces, events, basic counting, exponential approximation
**Chapter 2, Lab 2: The fundamentals: addition and multiplication rules, conditioning and Bayesβ 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, marginals, conditionals, independence**- Section 5.3.1 Section 5.4: Random permutations and symmetry

### Expectation

**Chapter 8, Lab 3B: 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****Section 9.2**, Section 9.3: Expectation by conditioning, applications to waiting times in i.i.d. Bernoulli trials

### Random Counts

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

- Section 8.1: Bernoulli
- Section 8.1: Uniform on a, a+1, β¦ , b
- 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, Chapter 7, Sections 8.2, 8.3, 8.4: Poisson and related expectations
- Sections 8.2, 9.3: Geometric, its right hand tail, and its expectation