## Course webpage

### Instructor

**Email:** parsiad (at) umich (dot) edu

### Lectures

**Section 1:**TuTh 10:00AM - 11:30AM in 1640 CHEM**Section 2:**TuTh 01:00PM - 02:30PM in 4096 EH

### Office hours

- Tu 11:30AM-01:00PM in 1842 EH
- Th 03:00PM-04:30PM in 1842 EH

### Course description

This is a fairly rigorous introduction to probability theory with some emphasis given to both theory and applications, although a knowledge of measure theory is not assumed. Topics covered are: probability spaces, conditional probability, discrete and continuous random variables, generating functions, characteristic functions, random walks, branching processes, limit theorems.

### Prerequisites

Math 451 required.

### Textbook

(Optional) Walsh, John B. Knowing the odds: an introduction to probability. Vol. 139. American Mathematical Soc., 2012.

### Grading

The grading scheme is as follows:

- Assignments: 20%
- Midterms: 40%
- Final: 40%

The lowest of your assignment scores will not count towards your final grade. Midterms will be held in class. The final is on **April 23rd, 1:30 - 3:30 pm** (room TBA).

Grades will be posted on Canvas:

**Section 1:**https://umich.instructure.com/courses/207895**Section 2:**https://umich.instructure.com/courses/194654

## Assignments

All assignments are to be handed in at the *beginning* of class.

- Assignment 1: due Tu Jan 16 (solutions now included)
- Assignment 2: due Tu Jan 23
- Assignment 3: due Tu Jan 30

## Lecture notes

- Th Jan 4: sample spaces, sigma-algebras, and probability measures (Sections 1.1 and 1.2)
- Tu Jan 9: conditional probability, independence, counting, generating a sigma-algebra, and Borel sets (Sections 1.4 to 1.7)
- Th Jan 11: random variables, distribution functions, indicator random variables, Borel measurable functions (Section 2.1)
- Tu Jan 16: uniform distribution, existence of random variables, independence of random variables, types of distributions (Section 2.2 to 2.4)
- Th Jan 18: expectations and variances of discrete random variables (Section 2.5 and 2.6)
- Tu Jan 23: moments, moment generating functions, and special discrete distributions (Section 2.6 and 2.8)
- Th Jan 25
- Tu Jan 30
- Th Feb 1
- Tu Feb 6
- Th Feb 8
- Tu Feb 13
- Th Feb 15:
**midterm exam 1**(in class) - Tu Feb 20
- Th Feb 22
- Tu Feb 27: no class
- Th Mar 1: no class
- Tu Mar 6
- Th Mar 8
- Tu Mar 13
- Th Mar 15
- Tu Mar 20:
**midterm exam 2**(in class) - Th Mar 22
- Tu Mar 27
- Th Mar 29
- Tu Apr 3
- Th Apr 5
- Tu Apr 10
- Th Apr 12
- Tu Apr 17

## Miscellany

You are not expected to know any material in this section for assignments/exams.

- It was asked in class if the principle of inclusion-exclusion can be extended to countably many events. The answer seems to be yes, but with some technical conditions. See, e.g., Friedland, Shmuel, and Elliot Krop. “Exact conditions for countable inclusion-exclusion identity and extensions.”