D. Probability Reference

The quantum-relevant subset. Distributions: pᵢ ≥ 0, Σpᵢ = 1; quantum outcome distributions are pᵢ = |αᵢ|². Expectation: ⟨O⟩ = Σ pᵢoᵢ; quantum version ⟨ψ|O|ψ⟩ for observable O with eigenvalues oᵢ. Variance σ² = ⟨O²⟩−⟨O⟩²; standard error of an N-shot mean: σ/√N — the shot-budget formula (Ch. 16.10): to estimate a probability to ±δ needs N ≈ p(1−p)/δ² shots. Conditional: P(A|B) = P(A∩B)/P(B); measurement collapse is conditioning in disguise. Bayes: P(H|E) ∝ P(E|H)P(H) — decoder belief updating (Ch. 36) is Bayes on syndromes. Correlation vs. causation, quantum edition: entangled correlations exceed classical bounds (Bell) yet signal nothing (Ch. 2.10) — the one place naive probability fails and quantum probability takes over. Sampling: multinomial for shot outcomes; bootstrapping over seeds for error bars on benchmarks (Ch. 46.8). Distributions you'll meet: binomial (k successes in n shots), Gaussian (CLT limit), exponential (T1 decay), Poisson (rare-event counts — dark counts in Ch. 65 detectors).