MIT OpenCourseWare
Probability and Random Variables
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructor
- Prof. Scott Sheffield
- Term
- Fall 2019
- Level
- Undergraduate
- What's inside
- 10 problem sets · 27 exams · 27 solutions · 1 lecture note · 1 reading · 39 other files · 5 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.600 Probability and Random Variables, Fall 2019, Prof. Scott Sheffield — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: none is claimed; materials are grouped by MIT's own sections. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Has MIT solutions
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- MIT lists a session calendar for this course, but it could not be verified well enough to build a sequence from it — materials are grouped by section instead.
Not included here
26 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (24 items)
- Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (2 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Instructor Insights
Readings
Lecture Notes
37 files
- Multinomial coefficients and more counting Download
- Sample spaces and set theory Download
- Axioms of probability Download
- Probability and equal likelihood Download
- Conditional probabilities Download
- Bayes’ formula and independent events Download
- Discrete random variables Download
- Binomial random variables, repeated trials and the so-called modern portfolio theory Download
- Poisson random variables Download
- Poisson processes Download
- More discrete random variables Download
- Review for midterm exam 1 Download
- Continuous random variables Download
- Normal random variables Download
- Exponential random variables Download
- More continuous random variables Download
- Joint distribution functions Download
- Sums of independent random variables Download
- Covariance and some conditional expectation exercises Download
- Conditional expectation Download
- Moment generating functions Download
- Weak law of large numbers Download
- Review for midterm exam 2 Download
- Central limit theorem Download
- Strong law of large numbers and Jensen’s inequality Download
- Markov chains Download
- Martingales and the optional stopping time theorem Download
- Risk neutral probability and Black-Scholes Download
- Review for final exam I Download
- Review for final exam III Download
- 18.600 F2019 Lecture 1: Permutations and combinations Download
- 18.600 F2019 Lecture 9: Expectations of discrete random variables Download
- 18.600 F2019 Lecture 10: Variance and standard deviation Download
- 18.600 F2019 Lecture 23: Conditional probability, order statistics, Download
- 18.600 F2019 Lecture 33: Entropy Download
- 18.600 F2019 Lecture 35: Martingales and risk neutral probability Download
- 18.600 F2019 Lecture 37: Review for final exam II Download
Assignments
11 files
- 18.600 Probability and Random Variables F2019, Doob’s Optional Stopping Theorem Download
- 18.600 Probability and Random Variables F2019, Problem Set 1 Download
- 18.600 Probability and Random Variables F2019, Problem Set 2 Download
- 18.600 Probability and Random Variables F2019, Problem Set 3 Download
- 18.600 Probability and Random Variables F2019, Problem Set 4 Download
- 18.600 Probability and Random Variables F2019, Problem Set 5 Download
- 18.600 Probability and Random Variables F2019, Problem Set 6 Download
- 18.600 Probability and Random Variables F2019, Problem Set 7 Download
- 18.600 Probability and Random Variables F2019, Problem Set 8 Download
- 18.600 Probability and Random Variables F2019, Problem Set 9 Download
- 18.600 Probability and Random Variables F2019, Problem Set 10 Download
Exams
53 files
- Fall 2011 18.440 Midterm Exam 1 Download
- Fall 2011 18.440 Midterm Exam 1 Solutions Download
- Fall 2011 18.440 Midterm Exam 2 with Solutions Download
- Fall 2012 18.440 Final Exam Download
- Fall 2012 18.440 Final Exam Solutions Download
- Fall 2012 18.440 Midterm Exam 1 Download
- Fall 2012 18.440 Midterm Exam 1 Solutions Download
- Fall 2012 18.440 Midterm Exam 2 Download
- Fall 2012 18.440 Midterm Exam 2 Solutions Download
- Fall 2019 18.600 Final Exam Download
- Fall 2019 18.600 Final Exam Solutions Download
- Fall 2019 18.600 Midterm Exam 1 Download
- Fall 2019 18.600 Midterm Exam 1 Solutions Download
- Fall 2019 18.600 Midterm Exam 2 Download
- Fall 2019 18.600 Midterm Exam 2 Solutions Download
- Spring 2011 18.440 Final Exam Download
- Spring 2011 18.440 Final Exam Solutions Download
- Spring 2011 18.440 Midterm Exam 1 Download
- Spring 2011 18.440 Midterm Exam 1 Solutions Download
- Spring 2011 18.440 Midterm Exam 2 Download
- Spring 2011 18.440 Midterm Exam 2 Solutions Download
- Spring 2014 18.440 Final Exam Download
- Spring 2014 18.440 Final Exam Solutions Download
- Spring 2014 18.440 Midterm Exam 1 Download
- Spring 2014 18.440 Midterm Exam 1 Solutions Download
- Spring 2014 18.440 Midterm Exam 2 Download
- Spring 2014 18.440 Midterm Exam 2 Solutions Download
- Spring 2016 18.600 Final Exam Download
- Spring 2016 18.600 Final Exam Solutions Download
- Spring 2016 18.600 Midterm Exam 1 Download
- Spring 2016 18.600 Midterm Exam 1 Solutions Download
- Spring 2016 18.600 Midterm Exam 2 Download
- Spring 2016 18.600 Midterm Exam 2 Solutions Download
- Spring 2017 18.600 Final Exam Download
- Spring 2017 18.600 Final Exam Solutions Download
- Spring 2017 18.600 Midterm Exam 1 Download
- Spring 2017 18.600 Midterm Exam 1 Solutions Download
- Spring 2017 18.600 Midterm Exam 2 Download
- Spring 2017 18.600 Midterm Exam 2 Solutions Download
- Spring 2018 18.600 Final Exam Download
- Spring 2018 18.600 Final Exam Solutions Download
- Spring 2018 18.600 Midterm Exam 1 Download
- Spring 2018 18.600 Midterm Exam 1 Solutions Download
- Spring 2018 18.600 Midterm Exam 2 Download
- Spring 2018 18.600 Midterm Exam 2 Solutions Download
- Spring 2019 18.600 Final Exam Download
- Spring 2019 18.600 Final Exam Solutions Download
- Spring 2019 18.600 Midterm Exam 1 Download
- Spring 2019 18.600 Midterm Exam 1 Solutions Download
- Spring 2019 18.600 Midterm Exam 2 Download
- Spring 2019 18.600 Midterm Exam 2 Solutions Download
- 18.600 Practice Final Exam Download
- 18.600 Practice Final Exam Partial Solutions Download
Other materials from this course
MIT OpenCourseWare, Prof. Scott Sheffield, 18.600 Probability and Random Variables, Fall 2019.
License: CC BY-NC-SA 4.0 · Edition: Fall 2019 · Open the original course on OCW ↗
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Per-resource rights are recorded on each resource; All-Rights-Reserved items are link-only, never mirrored.
