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.
Build my 18.600 study planWhat 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
Support, story, expectation, variance, and how it arises from simpler pieces — for every distribution on the syllabus. 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.
- 5
Put the volume on autopilot with Fennie
Upload the 18.600 syllabus or your OCW-based plan and Fennie's Daily Plan schedules same-day problem practice after each lecture topic, with distribution-story flashcards generated from the actual course materials. Free to start.
Start my 18.600 plan free
How Fennie helps with 18.600
Fennie's Daily Plans schedule 18.600 as same-day problem practice after every lecture — the only reliable cure for probability's lecture-comprehension illusion. Chat through why a conditioning decomposition works, and drill the named distributions as stories with auto-generated flashcards.
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?
It's one of the standard recommendations — the distribution fluency, expectation tricks, and martingale introduction map directly onto quant interview material.
Pass 18.600 with a plan, not a cram
Upload your 18.600 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.
Get started freeMore MIT courses
18.01 — Single Variable Calculus
18.01 is MIT's single-variable calculus GIR — limits, differentiation, integration, and infinite series — required of every MIT student without prior credit. The OCW version, including David Jerison's lectures, has taught calculus to millions of self-learners.
18.02 — Multivariable Calculus
18.02 is MIT's multivariable calculus GIR: vectors, partial derivatives, multiple integrals, and vector calculus through Green's, Stokes', and the divergence theorems. It's required for every MIT student and is among the most-viewed math courses on OpenCourseWare.
18.06 — Linear Algebra
18.06 is MIT's linear algebra course, made world-famous by Gilbert Strang, whose OCW lectures are arguably the most beloved math course recordings ever published. It covers systems of equations, vector spaces, orthogonality, determinants, eigenvalues, and the SVD with Strang's signature intuition-first style.
18.03 — Differential Equations
18.03 is MIT's differential equations course — first and second order ODEs, Laplace transforms, Fourier series, and linear systems — required by most engineering and science majors and among the most-used math courses on OpenCourseWare, where Arthur Mattuck's lectures are a classic.