Title: Week 7 — the same question, wearing a hundred costumes
Course: Introduction to Statistics (18-Week Generic Edition)

Hi everyone,

Quick quiz before the quiz: what do these have in common — 5 marketing emails each clicked with probability 0.2, four free throws from a 50-50 shooter, and guessing your way through a true/false quiz? Answer: they are the same problem. Fixed number of tries, each a yes/no, count the wins. This week that pattern gets its famous name — the binomial distribution — and you get the whole toolkit: a checklist to recognize it (B·I·N·S), a formula for exact chances (ways × wins × losses), a two-number summary (expect np, give or take √(np(1−p))), and a spreadsheet function that does the heavy lifting (=BINOM.DIST).

Last week you built distributions row by row and earned E(X) the long way. This week's machine generates all of it from two numbers — and when we check the shortcut against your Week 6 method, they'll agree to the decimal. That's the fun of it.

Three things not to miss: 1. Chapter 7 is your primary reading — start there; the whole week's toolkit is built in it, piece by piece. 2. Data Lab 7 — "Two Hundred Rounds of Four" — you'll simulate 200 four-shot rounds of a 50-50 shooter and put the formula's predictions on trial against your own data. Due at the end of Week 7. 3. Discussion 7 — "The Hot-Hand Question" — is a hot streak real, or is it just what an unchanging p looks like? Initial post two days before the week ends, so classmates have time to reply.

One promise: nothing this week is new muscle — it's Week 5's independence and Week 6's expected value bolted together into your first named machine. And one tease: near the end of the week, watch what happens to binomial histograms as n grows. A curve is coming next week — the most famous shape in statistics — and you'll see its silhouette first.

Open the Start Here / Module Overview page first — it lays out everything in order with points and due dates. Bring a streak you believe in (or one you're suspicious of) to the first session.

See you in the course!