MIT 18.05: Introduction to Probability and Statistics
18.05 is MIT's introduction to probability and statistics: probability models, random variables, Bayesian and frequentist inference, and regression, taught in a celebrated flipped, problem-centered format whose complete materials on OCW make it one of the most recommended statistics self-study courses anywhere.
Fennie is independent and not affiliated with MIT. This is an unofficial study guide.
What makes it hard
Probability problems punish plausible-sounding reasoning like no other subject; conditioning errors feel correct right up until the answer is wrong. The Bayesian-versus-frequentist arc in the second half is conceptually deep: computing both kinds of answers is easy, keeping their interpretations straight is the actual work.
What you'll cover
- • Probability models and counting
- • Conditional probability and Bayes' theorem
- • Random variables and distributions
- • Bayesian inference
- • Frequentist inference and hypothesis testing
- • Confidence intervals and regression
The 18.05 study guide
How to study for MIT 18.05, step by step.
- 1
Do the in-class problems, not just the readings
18.05's flipped design means the problem sessions are the course. Self-learners on OCW should work every class-slide problem cold before reading its solution; skipping them hollows the course out.
- 2
Write the conditioning explicitly, every time
Most probability errors are silent conditioning errors. Forcing yourself to write P(A given B) with both pieces named catches the mistake while it's still visible.
- 3
Keep a Bayesian-frequentist phrasebook
Write side by side what a posterior probability claims versus what a confidence interval claims, and revisit the pair each unit. The conceptual distinction is the second half's real content.
- 4
Simulate when intuition argues with the math
A ten-line simulation settles probability disputes instantly and builds the intuition for next time. The course's own materials model this habit; adopt it.
Today
Today's 18.05 plan
What a Fennie Daily Plan looks like for 18.05. 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 18.05 good for self-study?
Yes, it's one of the best statistics courses on OCW: complete readings, problem slides with solutions, psets, and exams. The flipped format translates unusually well to self-pacing.
Is 18.05 hard?
The math is gentler than 18.600's, but probability reasoning itself is treacherous; conditioning errors feel correct. Problem volume, not lecture review, is what builds reliability.
18.05 or 18.600?
18.05 covers probability plus statistical inference at moderate mathematical depth; 18.600 is deeper, harder probability theory without the statistics. Data-science-bound students often want 18.05 first.
More MIT courses
18.01: Single Variable Calculus
18.01 is MIT's single-variable calculus GIR, covering 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, covering first and second order ODEs, Laplace transforms, Fourier series, and linear systems. It's required by most engineering and science majors and among the most-used math courses on OpenCourseWare, where Arthur Mattuck's lectures are a classic.