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Linear AlgebraMediumMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Medium problem

A support ticket is in Level 1 or Level 2 until it is Resolved (absorbing). Each hour, a Level 1 ticket stays at Level 1 with probability 1/41/4, is escalated to Level 2 with probability 1/21/2, and is resolved with probability 1/41/4. A Level 2 ticket is sent back to Level 1 with probability 1/41/4 and is resolved with probability 3/43/4. Starting at Level 1, what is the expected number of hours until the ticket is resolved? Express your answer as a common fraction.