Notes

The weekly instructional spine

The notes are the backbone of the course. There is one note per week, and reading the current week’s note before class — and again after — is the single most reliable way to keep up. Every note follows the same shape, so once you learn to read one, you can read them all.

How to read a week

Each weekly note is built from the same parts, in the same order. Knowing the anatomy lets you skim for what you need and study with intent:

  • The week question. A single question that the week exists to answer. Hold it in mind as you read; everything else is in service of it.
  • Concept development. The core ideas, built up in a few short sections from intuition toward precise statements. This is the part to read slowly.
  • Worked examples. Each idea is worked twice — once symbolically, once with numbers — including a slice of the recurring commuter’s-morning case (Maya, the shuttle, the weather, the quiz) plus one transfer example in a fresh context, so you see the idea move.
  • A common mistake. The error students most often make on this topic, named plainly so you can watch for it in your own work.
  • Ungraded self-checks. A few low-stakes practice prompts to test yourself. These are self-check only — no points, no submission.
  • Reading pointer. Where to read more: the relevant Grinstead & Snell chapter and, where useful, the MIT 18.05 page, with the reminder that these notes are the course’s own synthesis.
  • Looking ahead. A sentence or two connecting this week to the next, so the arc stays visible.

Keep the notation glossary and the distribution reference open alongside the notes.

The five parts

The fifteen weeks fall into five parts. Each part has a job, and the weeks within it build on one another.

Part I — Foundations of uncertainty. What a probability is, how to model a random situation, and the rules for combining events.

  1. Week 1 — Uncertainty, probability & models
  2. Week 2 — Sample spaces, events & rules

Part II — Conditioning & Bayesian reasoning. How a probability changes once you learn something, and how to invert that reasoning to update a belief.

  1. Week 3 — Conditional probability
  2. Week 4 — Independence & information
  3. Week 5 — Bayes’ rule & updating

Part III — Counting & discrete random variables. Counting outcomes, then packaging randomness into discrete random variables and their standard models.

  1. Week 6 — Counting & discrete probability
  2. Week 7 — Discrete random variables
  3. Week 8 — Expectation & variance
  4. Week 9 — Common discrete models

Part IV — Continuous variables & joint behavior. Moving from counts to measurements, where probability is area under a density, and then to pairs of quantities that vary together.

  1. Week 10 — Continuous random variables
  2. Week 11 — Common continuous models
  3. Week 12 — Joint distributions & dependence

Part V — Limits, simulation & synthesis. How averages and sums behave in the large, then a modeling project and a synthesis of the whole arc.

  1. Week 13 — Sums, simulation & limit behavior
  2. Week 14 — Probability modeling project
  3. Week 15 — Final review & synthesis

Public vs. graded

These notes and the practice in them are public and ungraded — study material only. No graded prompts, answer keys, rubrics, point values, or due dates appear on this site. Graded checkpoints, quizzes, homework, labs, the midterm, the project, and the final live in Blackboard (the LMS), which is authoritative for due dates, submissions, and grades. If this page and Blackboard ever disagree, follow Blackboard.