Question

Consider an urn initially containing N є N balls. For n E Z+, let Xn be the number of balls in the urn after performing the following procedure n times. If the urn is non-empty, one of the balls is removed at random. A fair coin is flipped, and if the coin lands tails then the ball is returned to the urn. If the coin lands heads, the ball is not returned. If the urn is empty, then the coin is flipped. If it lands tails, then N balls are returned to the urn. If it lands heads, then nothing happens. (a) (4p) Determine the transition matrix of the Markov chain (Xn)xo on E := {0, ,N} (b) (16p) What is the distribution of Xn as n → o?

Answer 1

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