Syllabus Math 351 Introduction to Probability and Statistics II

Holt Hall 171 MWF 10 - 10.50am

Contact Information

Edward A. Roualdes (call me Edward)


Office hours: Holt 204 Monday 2 – 3, Tuesday 9 – 10, and Thursday 2 – 3

Course Description

Continuation of MATH 350. Basic concepts of probability theory, random variables and their distributions, limit theorems, sampling theory, topics in statistical inference, regression, and correlation.

Student Learning Objectives / Goals

  • Introduce the language of statistics
  • Build understanding of random variables and their distributions
  • Learn how probability connects to statistics, and statistics connects to data
  • Introduce properties of statistics and sampling distributions


We will primarily use various chapters from Probability and Statistics - The Science of Uncertainty, Second Edition. This book is freely available as a PDF online, at the link above, hosted by the second author, Jeffrey S. Rosenthal.

If you would like to buy a book, please consider any one of the following:

Only the free PDF linked above is required, none of the books are required.

Additional Requirements

  • Access to a computer will be essential to master the material of this course. If you don’t have immediate and consistent access to a laptop, please speak to me as soon as possible.

  • We will learn to code in R using the programming environment RStudio Desktop, both of which are free software.

Content Delivery

Lectures are in person at the times listed above. No recordings will be available. As Gil Scott-Heron says, the revolution will not be televised; this class will be live.

All course materials will be posted to my website:

Course Communication

The absolute best place to ask a question is during lecture. I understand, though, that not all students feel comfortable asking questions publicly.

If you prefer more private and in person communication, come to office hours.

If you prefer written and identifiable communication, email me at . If your questions become too complex for email, as judged by me, I reserve the right to ask you to come visit my office to receive your answers in person.

If you prefer written and anonymous communication, I have created an anonymous Google form named ask. If you intend to ask a question anonymously, please remember that this form is anonymous. The implications of this anonymity are greater than you might at first think; take a minute to think through how you want me to address you specifically, if I don’t know who you are. Further, there might be some questions I deem to not deserve a response. If you intend to give me feedback, please give constructive and respectful feedback. If at any point this form goes poorly, as judged by me, I reserve the right to take it down.

If for any reason I need to address everyone in the course, I will send you an email to your student email account, eg

Course Grading

Your final grade for this course will be given according to the \(+/-\) grading system, based on the following percentages and scale: \(90 - 100\), A; \(80 - < 90\), B; \(70 - < 80\), C; \(60 - < 70\), D; \(<60\), F.

Component Percentage
Worksheets 100%

Grades will be posted to a shared (between me and each of you, individually and exclusively) Google Sheets file.


All worksheets must be created using Quarto, compiled into HTML (preferred) or PDF, and uploaded to our shared Google folder. If you prefer to compile your worksheet, for your own records into Microsoft Word, you are more than welcome to, but I don’t want Word documents.

Worksheets will be part at home and part in class. This is part of the reason that access to a laptop is essential to this course.

Each worksheet should be uploaded into its own subfolder, called say worksheet 01 which itself is located within our shared Google folder.

Notice how I’m attempting to force you on proper computer organization. Folders should provide the context, not file names.

You can re-submit a worksheet that was previously submit on time after it was graded for up to 50% of your missed points back. Think of this as an attempt to correct some of your less-than-correct solutions. As an example, if you earned 80% on a Worksheet, you can re-submit this Worksheet with updated answers for a maximum of 10% added to your original score. Thus, you could obtain 90% on a worksheet for which you originally earned 80%.


There will be zero tests.

Make-Up Policy

Worksheets assignments can be submit late for a maximum of 50% credit. You can submit a worksheet as late up until the last day of the regular semester, Friday, May 12 at 11:59pm.

You can not re-submit a submit-late Worksheet.

Diversity Policy

Respect: Students in this class are encouraged to speak up and participate during class meetings. Because the class will represent a diversity of individual beliefs, backgrounds, and experiences, every member of this class must show respect for every other member of this class (this includes me).

Academic Integrity Policy

Students are permitted and encouraged to collaborate on all assignments other than tests. However, each student must turn in their own work. Further, it is the expressed expectation of this instructor that all students demonstrate integrity and individual responsibility in all actions related to this course. Unethical behavior of any kind is unacceptable and will be prosecuted vigorously. Any sign of cheating in any way on any course assignment will be addressed directly, according to University standards. If you do not understand what plagiarism is, or what cheating entails, you must seek information regarding this matter from the current University Catalog and from me. The consequences of plagiarism begin with a failing grade on the work, and possibly a failing grade in the course, depending upon University action. More information is found on the Student Conduct, Rights, and Responsibilities campus webpage.

Disability Support

If you have any disability related needs, please contact Disability Support Service (Colusa Hall 898-5959 or campus information 898-INFO for directions) on campus to obtain the appropriate documentation. Afterwards, email me to identify your needs within the first two weeks of class so that any necessary arrangements can be made.

Confidentiality and Mandatory Reporting

As an instructor, one of my responsibilities is to help create a safe learning environment on our campus. I am required to share information regarding sexual misconduct with the University. Students may speak to someone confidentially by contacting the Counseling and Wellness Center (898-6345) or Safe Place (898-3030). Information on campus reporting obligations and other Title IX related resources are available here:

Course Outline

  1. Recap MATH 350
    • random variables
    • distributions and density functions
    • R: scatter and line plots, and histograms
    • expectations
    • independence
    • likelihood
  2. Expectations of the Sample Mean
    • mean, variance, bias
    • mean squared error
  3. Central Limit Theorem
    • Normal distribution theory
    • mathematics
    • simulations
  4. Inference
    • likelihood inference
    • Bayesian inference
  5. Linear Models
    • single mean model
    • multiple mean model
    • linear regression
    • bootstrap