Title: Week 6 — what is a chance actually worth?
Course: Introduction to Statistics (18-Week Generic Edition)

Hi everyone, and welcome to Week 6!

Last week you put numbers on chance — the probability a card, a roll, or a customer goes one way or the other. This week, chance gets a price tag. A $1 claw-machine play that might pay $10. A $30 protection plan that might cover a $120 replacement. A raffle ticket. This week's machinery — random variables and expected value — tells you what any of those deals is really worth, and it's the exact math insurance companies and arcades use to price them.

This week — Random Variables — we tackle the big question: when an uncertain outcome has numbers attached, what is it worth, and how wildly does it swing? By the end of the week you'll compute a deal's long-run value E(X), measure its wobble with the SD, and know what happens when fees are subtracted or rates multiplied.

Three things not to miss: 1. Chapter 6 is your primary reading — start there; the claw machine on page one carries the whole week. 2. Data Lab 6 has your spreadsheet run a raffle: you'll compute what a ticket is worth by formula, then simulate 1,000 draws and watch the long-run average walk right up to your answer. Due at the end of Week 6. 3. Discussion 6 — "The Warranty Question" — is an extended warranty ever the smart buy? Your initial post is due two days before the week ends, so classmates have time to reply.

One heads-up: the expected value has a famous twist — it's usually a value that can't actually happen on any single play. That's not a bug, and by mid-week you'll be explaining why to your chatbot (which will get it wrong).

Open the Start Here / Module Overview page first — it lays out everything in order with due points. Bring an opinion to the first session: would you play a $1 claw machine that pays out 80 cents?

See you in the course!