Stationary Distribution Interview Questions
Stationary distribution interview prep for long-run state probabilities, balance intuition, two-state examples, and Markov-chain mistakes.
Candidates extending Markov-chain basics into long-run behavior.
Long-run state mix
A stationary distribution is a set of state probabilities that stays the same after one transition of the Markov chain.
Balance intuition
In a stationary mix, probability flowing out of states is balanced by probability flowing in. For small chains, this balance can be easier than matrix notation.
Two-state example
For a two-state chain, write the probability of being in state A after one transition in terms of the current probabilities, then solve for the probability that reproduces itself.
Stationary is not starting
The starting distribution is where the process begins. A stationary distribution is a distribution that would remain unchanged if used as the starting distribution.
Convergence caution
Not every chain converges nicely to a stationary distribution from every start. Interview prompts usually use simple finite chains, but conditions still matter.
Common mistakes
Candidates often solve for a stationary distribution and immediately call it the current distribution. Say whether you are discussing now, after one step, or long-run behavior.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.