vibed/edu/.beans/edu-a1al--markov-lesson-transition-probabilities-and-matrice.md

title	status	type	priority	created_at	updated_at
Markov lesson: Transition Probabilities and Matrices	completed	task	high	2026-03-10T23:30:00Z	2026-03-10T23:30:00Z

Write Section 3 of edu/markov.md: 'Transition Probabilities and Matrices'\n\nLearning objectives:\n- Formally define the transition matrix P where P[i][j] = P(next=j | current=i)\n- Explain the stochastic matrix constraint: all rows sum to 1, all entries ≥ 0\n- Show how to compute the distribution after k steps: π₀ Pᵏ\n- Work through a 2×2 weather-model example by hand\n\nContent to produce:\n- 3–5 paragraphs of prose\n- A worked numeric example (2-state weather chain)\n- LaTeX-style or plain-text matrix notation\n- No code in this section\n\nTarget: replace the stub in edu/markov.md §3