← STAT 02360 · Probability and Random Variables
STAT 02360 · Probability foundations
Axioms, conditional probability, Bayes
Definition
Kolmogorov axioms: P≥0, P(Ω)=1, countable additivity for disjoint events. Conditional: P(A|B)=P(A∩B)/P(B). Bayes updates beliefs: P(H|D)∝P(D|H)P(H).
Read this
Draw tables/trees before formulas. Total probability law partitions the sample space.
Bayes: posterior ∝ likelihood × prior — normalize by P(D).
Complement rule P(Aᶜ)=1−P(A) is a constant timesaver.
Drill with flashcards
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Try this
Attempt each problem first, then open the worked solution.
1.Two-way table: compute a conditional probability and one Bayes update.