Level 5: Markov chains
Stationary distributions, hitting times, recurrence, and ergodicity — the state-machine reasoning behind regime models and queueing.
36 problems
First 5 free · rest Premium
- 1→
Stationary Distribution of a Two-State Chain
●●○○○Easy~4 min
- 2→
Winning from Deuce
●●●○○Medium~5 min
- 3→
Frog on the Lily Pads
●●●●○Hard~7 min
- 4→
Random Walk on a Graph
●●●○○Medium~6 min
- 5→
The Ehrenfest Urn
●●●●○Hard~7 min
- 6Premium
Limiting vs. Stationary Distributions
●●●○○Medium~5 min
- 7Premium
Expected Steps to Absorption
●●●●○Hard~7 min
- 8Premium
Random Walk on a Ring
●●●○○Medium~6 min
- 9Premium
A Birth-Death Queue
●●●●○Hard~7 min
- 10Premium
Mean First Passage in a Two-State Chain
●●○○○Easy~3 min
- 11Premium
Why PageRank Teleports
●●●○○Medium~5 min
- 12Premium
Reversible or Not?
●●●○○Medium~5 min
- 13Premium
Escaping the Maze
●●●○○Medium~6 min
- 14Premium
Will the Family Line Die Out?
●●●●○Hard~7 min
- 15Premium
Designing a Chain for a Target
●●●●○Hard~7 min
- 16Premium
How Many Shuffles Mix a Deck?
●●●○○Medium~5 min
- 17Premium
Random Walk on the Hypercube
●●●●○Hard~6 min
- 18Premium
Solving for a Stationary Distribution
●●●○○Medium~6 min
- 19Premium
Visiting Every Vertex
●●●●○Hard~7 min
- 20Premium
The Period of a State
●●○○○Easy~4 min
- 21Premium
Reaching a Target on K_n
●●●○○Medium~5 min
- 22Premium
Counting Visits Before Absorption
●●●○○Medium~6 min
- 23Premium
Long-Run Fraction of Time
●●○○○Easy~4 min
- 24Premium
Random Walk on a Star
●●●○○Medium~6 min
- 25Premium
Traversing a Line
●●●○○Medium~6 min
- 26Premium
Random Walk on a Weighted Graph
●●●○○Medium~5 min
- 27Premium
Commute Times and Resistance
●●●●○Hard~7 min
- 28Premium
The Renewal-Reward Theorem
●●●●○Hard~6 min
- 29Premium
Spectral Gap and Mixing Speed
●●●○○Medium~5 min
- 30Premium
Multi-Step Transition Probabilities
●●○○○Easy~4 min
- 31Premium
The Poisson Process
●●●○○Medium~6 min
- 32Premium
Little's Law
●●●○○Medium~5 min
- 33Premium
Continuous-Time Markov Chains
●●●●○Hard~6 min
- 34Premium
General Birth–Death Stationary Law
●●●●○Hard~6 min
- 35Premium
Hidden Markov Models
●●●○○Medium~6 min
- 36Premium
Merging and Splitting Poisson Streams
●●●○○Medium~5 min