HarvardX: STAT110x Introduction to Probability

STAT110x: Introduction to Probability

A comprehensive introduction to probability as a language and toolbox for understanding statistics, science, risk, and randomness.

The world is replete with randomness and uncertainty; probability and statistics extends logic into this realm. In this course, you will learn ideas and tools needed to understand the data and randomness that arise in many areas of science, engineering, economics, and finance.

This course aims to provide a strong foundation for future study of statistical inference, stochastic processes, machine learning, randomized algorithms, econometrics, and other subjects where probability is needed.

Portions of the course material were adapted from Introduction to Probability (second edition) by Joseph K. Blitzstein and Jessica Hwang, Chapman & Hall/CRC Press (2019), ISBN 9781138369917, used with permission. A free online version of the book (non-downloadable) is available at http://probabilitybook.net. If you're interested in purchasing a print copy of the book, please visit the publisher's website (linked above) or Amazon.com.

Prerequisites: All units require knowledge of algebra; Units 4-6 require single variable calculus (derivatives and integrals); Unit 7 requires familiarity with matrices. No previous background in probability or statistics is required.

Course Material and Schedule

This course has seven units of content, after a short introduction and orientation. A course map is available to help navigate the material.

• Unit 0: Introduction and Course Orientation
• Unit 1: Probability, Counting, and Story Proofs
• Unit 2: Conditional Probability and Bayes' Rule
• Unit 3: Discrete Random Variables
• Unit 4: Continuous Random Variables
• Unit 5: Averages, Law of Large Numbers, and Central Limit Theorem
• Unit 6: Joint Distributions and Conditional Expectation
• Unit 7: Markov Chains

The course will end on June 30, 2020, and will then enter archive mode. The discussion forums will close to new posts and the staff will no longer be monitoring the course.

Assessments and Grading

Course Policies

This course is governed by the following policies. Be sure to read them carefully.

HarvardX Honor Code

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Discussion Forum Posting Policy

We encourage class participants to share their solutions and ideas for practice problems, whereas for homework problems, posting full solutions in the forums is not allowed. The staff will be proactive in removing posts and replies in the discussion forums that have stepped over the line.

• It is ok to discuss the general approach to solving a homework problem, without going into a lot of technical details.
• It is ok to ask for a hint, or several hints for that matter, if you get stuck while solving a homework problem. When asking for a hint, try to explain in general terms what you have tried and why you are stuck.
• It is NOT OK to take someone else's solution and simply copy the answers from their solution into your problem.
• It is NOT OK to take someone else's formula and plug in your own numbers to get the answer for any problem.
• It is NOT OK to post answers to any problem.
• It is NOT OK to look at someone else's full, step-by-step solution to any homework problem.

If you have collaborated with others in generating a correct solution to a problem, a good test to see if you were engaged in acceptable collaboration is to make sure that you are able to do the problem on your own.

Discussion Forum Guidelines

The discussion forum is the main way for you to communicate with the course team and other students. We hope it contributes to a sense of community and serves as a useful resource for your learning. Here are some guidelines to observe on the forums.

• Search Before Asking: The forum will be hard to use if there are multiple threads on the same issue. The best discussions happen when several people participate in a single thread. Before asking a question, use the search feature to see if someone else has already created this thread.
• Descriptive Titles: Try to compose a title which is descriptive and provides as much information as possible without being overly long: In your title, specify the problem or video and, in a few words, what your issue is. In the question text, describe what aspect you do not understand and what you have already tried doing.
• Organize your Discussions: When creating a post, be sure to choose a category (such as General, Tech Issues, or Python Help). If you have a question about a particular page or problem, include a link to that page.
• Write Clearly: We know that English is a second language for many of you but correct grammar will help others to respond. Avoid ALL CAPS, abbrv of wrds (abbreviating words), and excessive punctuation!!!!
• Encourage useful posts: This applies to both questions and responses. Click on the green plus button at the top right of the box for either a post or a response. In this way, useful posts can be found more easily.
• Be polite: We have learners from all around the world and with different backgrounds. Something that is easy for you may be challenging for someone else. Let's build an encouraging community.
• You can create mathematical expressions in the discussion forums by encasing LaTeX code in dollar signs.

Course staff can be contacted on the discussion forum by creating a new post with the word [STAFF] in the title. Issues will generally be addressed within 72 hours.

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Acknowledgements

Course Team

Joseph K. Blitzstein, Professor of the Practice in Statistics and Co-Director of Undergraduate Studies, Harvard University

HarvardX

• Colin Fredericks, Senior Project Lead
• Sarah Walkowiak, Project Lead
• Jen Walker, Video Editor
• Siobhan Landry, Video Editor
• Luis Duarte, Web App Developer

Content Developers

• Anqi Zhao, PhD
• Delphine Vendryes
• Ye Li
• Jeffrey Winning

Teaching Assistants

• Matt DiSorbo

Animation

• Rachel D'Erminio, Raetastic!, Animator and Illustrator

Animation Voices

• Jon Alper
• Raj Bhuptani
• Joe Blitzstein
• Stefan Esposito
• Colin Fredericks
• Zofia Gadjos
• Maria Kobrina
• Rob Lue
• Drew Lichtenstein
• Casey Roehrig
• Ana Trandafir
• Jared Van Halen
• Michele Zemplenyi

Interactive Programmers

• Richard Caloggero
• Jonah Elgart
• Colin Fredericks

Special Thanks

• The HarvardX Production, Technical and Finance Teams
• Harvard University Radcliffe Institute for Advanced Study
• Harvard University Statistics Department
• Kevin McGowan, Anthony DiBartolo, and the staff of the Harvard University Media Production Center
• Chapman & Hall/CRC Press
• Steffi Blitzstein
• William Chen
• Matt DiSorbo
• Jessica Hwang
• Rafael Irizarry
• John Kimmel
• Rob Lue
• Andrew Ho
• Dan Levy
• Sergiy Nesterko
• Kenneth Wang
• Annie Valva
• The students and teaching fellows of Stat 110