COMP 2302 · Data Science: Probability

Led by Pearlian Causality Simulacrum

Probability as a language for uncertainty — from sample spaces and combinatorics through distributions to Bayes' theorem and the limits of correlation.

1. Module 1

   Probability as a Language for Uncertainty

   Led by Pearlian Causality Simulacrum

   The question

   P(rain tomorrow) = 0.7 — is this a fact about the world or a statement about your knowledge? The frequentist and Bayesian interpretations disagree. What does each imply for how you should bet on the 11th coin flip?

   Outcome

   The student can apply the addition and multiplication rules and explain the two interpretations.

   Sub-units

   1. ○ 1.1 The Axioms and the Rules Open this unit → ✓ ↻
   2. ○ 1.2 Frequentist vs Bayesian Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   Combinatorics: Counting What Matters

   Led by Pearlian Causality Simulacrum

   The question

   The probability of winning Powerball is 1 in 292 million — not an estimate but a combinatorial calculation. Permutations, combinations, the multiplication principle. What does counting tell you that probability alone cannot?

   Outcome

   The student can apply all four counting formulas and connect combinatorics to cross-validation.

   Sub-units

   1. ○ 2.1 The Lottery Calculation Open this unit → ✓ ↻
   2. ○ 2.2 Essay: Combinatorics in ML Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   Probability Distributions: Discrete

   Led by Pearlian Causality Simulacrum

   The question

   Bernoulli, Binomial, Poisson — three distributions, each for a different kind of discrete random event. For each scenario (click-through, server arrivals, A/B tests), which distribution applies and what are its parameters?

   Outcome

   The student can identify and parameterise discrete distributions for data science scenarios.

   Sub-units

   1. ○ 3.1 Match the Distribution Open this unit → ✓ ↻
   Open this module → Print certificate of completion
4. Module 4

   Probability Distributions: Continuous

   Led by Pearlian Causality Simulacrum

   The question

   The normal distribution appears everywhere because of the central limit theorem — the sample mean of any distribution approaches normality as n grows. Why does this matter for statistical inference, and when does it break down?

   Outcome

   The student can use z-scores, explain the CLT, and identify when normality assumptions fail.

   Sub-units

   1. ○ 4.1 The Central Limit Theorem in Practice Open this unit → ✓ ↻
   Open this module → Print certificate of completion
5. Module 5

   Bayes' Theorem and Causal Reasoning

   Led by Pearlian Causality Simulacrum

   The question

   A disease is 1% prevalent. Your test is 95% sensitive and 90% specific. You test positive. The posterior probability of disease is probably not what you expect. And even when you compute it correctly, Pearl asks: does the test detect disease, or cause it?

   Outcome

   The student can apply Bayes' theorem and articulate the distinction between association and causation.

   Sub-units

   1. ○ 5.1 The Medical Test Problem Open this unit → ✓ ↻
   2. ○ 5.2 Final Essay: Association and Causation Open this unit → ✓ ↻
   Open this module → Print certificate of completion