Measure of Chance

A first course

Measure
of Chance

A first course in probability. From the counting you already know, to ideas used in clinics, games, polls, and models.

Raghu Ugare

LambdaMatters

raghu.ugare@gmail.comraghu.ugare@lambdamatters.com

Begin with the preludeTry a lab
A five-pip die resting on an open probability notebook, surrounded by a running-frequency plot, a bell curve, coins, and books by Bayes, Bernoulli, Gauss, and Markov

Contents

The course

Before the first die, we ask what “random” means. Then likelihood, information, and estimation arrive in the last third, prepared from the beginning. Along the way: mammograms, monsoon forecasts, insurance, cricket, courtrooms, and tigers.

  1. PreludeWhat Do We Mean by Random?
  2. ISample Spaces
  3. IIEvents and Axioms
  4. IIIConditional Probability
  5. IVBayes' Theorem
  6. VIndependence
  7. VIRandom Variables
  8. VIIExpectation and Variance
  9. VIIIDiscrete Families
  10. IXContinuous Chance
  11. XJoint Distributions
  12. XILimit Theorems
  13. XIILikelihood and Models
  14. XIIIEntropy and Information
  15. XIVEstimation
  16. XVMarkov Chains
  17. XVIPioneers
  18. XVIIParadoxes of Probability
  19. XVIIIFurther Reading

Work by hand

Labs & problems

Five interactive figures — a die, a clinic, a binomial, a settling average, a bell — make simulation a third language beside story and mathematics. The problem set mixes computation, modelling, proof, and deliberately surprising questions.

Problems & solutions

The inks

Pantone matching

Apricot paper, an emerald accent, and a spark of tangerine. Screen values after Peach Fuzz, Orange 021 C, and a forest green near 17-5641. Paper inks still live in a fan deck.

  • Emerald

    17-5641

  • Peach Fuzz

    13-1023

  • Tangerine

    Orange 021 C

  • Marigold

    near 134 C

  • Cloud Dancer

    11-4201