MIT 18.600: Probability and Random Variables
18.600, formerly 18.440, is MIT's core probability course: combinatorics, random variables, the named distributions, expectation, limit theorems, and martingales, taught with full mathematical depth. It's the standard probability foundation for math majors, quants-in-training, and 18.05 graduates who want the real machinery.
Fennie is independent and not affiliated with MIT. This is an unofficial study guide.
What makes it hard
Like every serious probability course, the gap between following lectures and solving problems is the difficulty: the problems demand choosing the right decomposition (conditioning, indicators, symmetry), and that instinct only comes from volume. The limit-theorem and martingale material at the end adds analysis-flavored rigor on top.
What you'll cover
- • Counting and combinatorics
- • Discrete and continuous random variables
- • Named distributions and their stories
- • Expectation, variance, and covariance
- • Moment generating functions
- • Law of large numbers and central limit theorem
- • Martingales
The 18.600 study guide
How to study for MIT 18.600, step by step.
- 1
Solve problems the same day as every lecture
Probability comprehension is an illusion until tested; the lecture always feels clear. Same-day problems convert the feeling into either skill or a useful list of what to ask about.
- 2
Drill the indicator-variable trick until reflexive
Linearity of expectation with indicators dissolves problems that look impossible, and 18.600 problems reach for it constantly. Collect every instance you meet and rework them cold.
- 3
Know each named distribution as a generative story
For every distribution on the syllabus, know the support, the story, the expectation, the variance, and how it arises from simpler pieces. Recognition of the story is how exam problems open.
- 4
Give the final units analysis-level care
Convergence arguments and martingales reward the precision habits of a proof course. Slow down, write the statements carefully, and rework the lecture examples by hand.
Today
Today's 18.600 plan
What a Fennie Daily Plan looks like for 18.600. Yours is built from your own syllabus and adapts every day to your deadlines and progress.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
FAQ
Is 18.600 hard?
Yes. The problems require creative decompositions, not formula application, and the late units bring real mathematical rigor. It's also the course that makes later statistics and finance math feel easy.
Is 18.600 the same as 18.440?
Yes. 18.440 was renumbered 18.600. Older OCW materials and most internet discussion use 18.440; the content lineage is the same.
Is 18.600 good for quant finance preparation?
Yes, it's one of the standard recommendations. The distribution fluency, expectation tricks, and martingale introduction map directly onto quant interview material.
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