Week 01
- Supplemental Notes – Logical operations, models, statistical regularity, axiomatic probability, set language, proof methods (18 pp)
- Addition Theorem – Standalone proof of \(P(A)+P(B)=P(A \cup B)+P(A \cap B)\) (3 pp)
Week 02
- Supplemental Notes – Rules of inference, independence, conditional probability, total probability, Bayes’ theorem, binary channel / MAP estimation (21 pp)
Week 03
- Supplemental Notes – Proof types, sigma-algebra IMAC example, discrete sample spaces, counting methods, birthday paradox, permutations, Stirling’s approximation, binomial coefficients/theorem (15 pp)
Week 04
- Supplemental Notes – Bernoulli/binomial, Stirling’s at peak, multinomial, sequences/series, convergence tests, geometric/negative binomial, hypergeometric, BEG CUP distribution selection (20 pp)
- Supplemental Notes (04b) – Poisson probability/law (derivation), alpha-decay and basketball examples, MGF preview, Poisson approximation accuracy, set sizes, Cantor’s theorem, cardinalities (6 pp)
Week 05
- Supplemental Notes (Part 1) – Random variables, PAM, PMF, CDF, cardinality/countability, continuous distributions, PDF, Uniform, Gaussian, Gaussian integral, normal table (pp 1–18)
- Supplemental Notes (Part 2) – Signal detection, trigonometry review, Cauchy, Gamma function, Exponential, Gamma pdf, Chi-square, Beta, Beta function proof (pp 19–34)
Week 06
- Supplemental Notes – Moments, expectation, LOTUS, variance, binomial/geometric/negative-binomial/uniform/Cauchy/normal/exponential/gamma/chi-square/beta moments, higher-order moment existence, indicator function moments (22 pp)