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5. (15 points) Four blue and four maize balls are distributed in two urns in such a way that each contains four balls. We say that the systern is in state i, i = (), 1, 2, 3, 4, if the first urncontains i maize balls. At each step, we draw one ba from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xn denote the state of the system after the nth step. Write the transition probability matrix of the Markov Chain X 0,1,2,..

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Soluthom e ball im υτη1 4-i maige hal i blue bal 4i blue ba ea iit m t 40 1 6 0 4 0 0 ) S

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