DISTRIBUTIONSSTARTER◉ LIVE LAB
Normal Distribution
Bell-curve averaging: many small independent effects sum to a predictable center with thin tails.
How it works
- Add up many small, unrelated nudges and the total piles up in the middle.
- Spread is set by σ: ~68% within 1σ, ~95% within 2σ.
- Standardize (z-scores) to compare apples and oranges.
Use → Use when errors aggregate. Don't use for rich-get-richer or contagious outcomes.
Watch out → Fat tails, feedback, or a handful of giants break the bell — check a histogram first.
Try it → Roll 5 dice 200 times and plot the totals: the bell appears from flat dice.
REDCAPE jobs → Reason · Predict · Communicate
Free sources → Coursera Model Thinking M2 (CLT) • OpenIntro Statistics (CC BY-SA)
INTERACTIVE LABoriginal recreation — poke it
MEAN
3.53
SPREAD (σ)
1.72
One die is flat. Average a few and a bell appears; the spread shrinks like 1/√n.
Attach to a lattice — combines with
Different families, shared jobs. Disagreement between them is where insight lives.
LINEAR & NONLINEAR
Categorical & Threshold Models
Buckets and cutoffs turn messy attributes into testable if-then rules.
SHARED JOBS: REASON · PREDICT · COMMUNICATE
DIFFUSIONBroadcast Model
One source reaches a fixed pool at a steady rate: fast early, then fading returns — the r-shaped curve.
SHARED JOBS: PREDICT · COMMUNICATE
LEARNINGDiversity Prediction Theorem
Crowd error equals average error minus diversity. Diverse models beat the lone genius.
SHARED JOBS: PREDICT · COMMUNICATE