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This is an online review for a standard introductory undergraduate probability and statistics course.

In many disciplines, such engineering, undergraduates are typically required to take one course on statistics and probability. By the time such a student reaches graduate school, much of that learning has been forgotten (or at least is hard to recall). The goal of this online course is to give a brief review of what was learned in an undergraduate statistics class. It includes video lectures, practice homework problems, and a practice "final exam". It doesn't cover every topic included in most full-semester statistics courses, but it does review the basics.

I teach a graduate engineering course called From Data to Decisions: Measurement, Uncertainty, Analysis, and Modeling. The goal of that course is to give graduate students the tools they need to properly handle data for the doctoral thesis and their careers. Generally, I have to spend three weeks reviewing undergraduate statistics just to get all of my students back up to speed, before starting the more advanced material. This online statistics review course takes those three weeks and puts them online.

Optional Textbooks: It will be useful to supplement these lectures with reading. If you have your undergraduate statistics text, use that. If not, there are many good texts. Here are a few:

- Richard A. Johnson, Miller and Freund’s Probability and Statistics for Engineers

Jay Devore, Probability and Statistics for Engineering and the Sciences

Jay Devore and Nicholas Farnum, Applied Statistics for Engineers and Scientists

Robert M. Bethea and R. Russell Rhinehart, Applied Engineering Statistics - Walpole, Myers, Myers, and Ye, Probability & Statistics for Engineers & Scientists
- Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability

And many others…

To "take" this online course, work through the links below to watch the lectures, do the homework, and take the practice final. If you pass the final exam at the end (and for graduate students, that means getting an 80% or better), then you are ready to move on to a more advanced statistics course.

(Hint: some people like watching the lectures at 1.25X or 1.5X speed. Try it.)

Lecture 0: Introduction (7 min) - hardcopy of the slides: StatReview_Intro.pdf

Lecture 1: What is Statistics? (27 min) - hardcopy of the slides: StatReview_Lecture01.pdf

Lecture 2: Descriptive Statistics, part 1 (14 min) - hardcopy of the slides: StatReview_Lecture02.pdf

Datasets to accompany lectures 2 & 3: StatReview_Lecture2&3.xlsx

Lecture 3: Descriptive Statistics, part 2 (18 min) - hardcopy of the slides: StatReview_Lecture03.pdf

Lecture 4: Probability, part 1 (29 min) - hardcopy of the slides: StatReview_Lecture04.pdf

Lecture 5: Probability, part 2 (26 min) - hardcopy of the slides: StatReview_Lecture05.pdf

Lecture 6: Probability, part 3 (28 min) - hardcopy of the slides: StatReview_Lecture06.pdf

Homework #1 (probability), Homework #1 solutions

Lecture 7: Discrete Random Variables (23 min) - hardcopy of the slides: StatReview_Lecture07.pdf

Lecture 8: Expectation Value and Variance (20 min) - hardcopy of the slides: StatReview_Lecture08.pdf

Lecture 9: Continuous Random Variables (23 min) - hardcopy of the slides: StatReview_Lecture09.pdf

Homework #2 (RVs, expectation, variance), Homework #2 solutions

Bonus problem: The Texas Lottery

Lecture 10: Sampling Distribution (25 min) - hardcopy of the slides: StatReview_Lecture10.pdf

Lecture 11: Confidence Intervals (38 min) - hardcopy of the slides: StatReview_Lecture11.pdf

Lecture 12: Hypothesis Testing (28 min) - hardcopy of the slides: StatReview_Lecture12.pdf

Digression on how p-values can be abused: Science isn't Broken

Lecture 13: Inferences About a Mean (19 min) - hardcopy of the slides: StatReview_Lecture13.pdf

Lecture 14: Inferences About a Variance (11 min) - hardcopy of the slides: StatReview_Lecture14.pdf

Homework #3 (inferences), Homework #3 solutions

Lecture 15: Correlation (17 min) - hardcopy of the slides: StatReview_Lecture15.pdf

Lecture 16: Linear Regression, part 1 (29 min) - hardcopy of the slides: StatReview_Lecture16.pdf

Lecture 17: Linear Regression, part 2 (28 min) - hardcopy of the slides: StatReview_Lecture17.pdf

Homework #4 (regression), Homework #4 solutions

Homework04.xlsx, Homework04_solution.xlsx

A brief review of this review: Statistics - the big picture.pdf

Formula sheets and tables:

Practice Final Exam, Practice Final Exam Solutions

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