The Long Run

Stationary distributions

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A stationary distribution satisfies πP = π.
• Two states: π_S = a/(a + b), balancing the flows.
• Long-run fraction of time in each state = its stationary probability.

Steps

1. A forecast that never changes
2. A drier climate
3. A frog on three lily pads
4. Check the balance
5. Time averages
6. Rainy days per year