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When I listen to music on my smartphone, the app decides to repeat a song with...

When I listen to music on my smartphone, the app decides to repeat a song with probability α ∈ (0, 1), or, if it doesn’t repeat, to randomly select one of the other N − 1 songs and play that instead. Find the limiting probability limn→∞ P(nth song is the same as the first song). Hint: Define a suitable two state Markov Chain with states {initial song, other song}.

math   Statistics-And-Probability   
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