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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

A three-state Markov chain has steady-state distribution π=(12,13,16)\boldsymbol\pi = \left(\tfrac12, \tfrac13, \tfrac16\right) and is irreducible. Starting in state 3, what is the expected number of steps until the chain first returns to state 3?