Replaces the stub with full lesson content:
- Defines the transition matrix P[i][j] and stochastic matrix constraints
- Derives multi-step probabilities via π_k = π₀ · P^k
- Works through the 2-state weather chain by hand (1- and 2-step calculations)
- Bridges to §9 stationary distributions
- Words as states paragraph
- Bigrams and transition tables explanation
- Worked bigram example with two-sentence corpus and transition table
- Why generated text sounds locally plausible but globally incoherent
- Order-n chains and the coherence/novelty tradeoff
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>