Question: Problem 1 (14 points). (a) Solve the difference equation uk +1 - 4x + x1 = 0 subject to the boundary conditions uo = 1

Problem 1 (14 points). (a) Solve the difference equation uk +1 - 4x + x1 = 0 subject to the boundary conditions uo = 1 and 410 = 0. Give the exact solution, i.e., do not round the coefficients A, and Ag. (b) In a gambler's ruin problem with p = player A begins with 8 units and player B begins with 2 units. Use your answer to (a) to determine the probability of ruin for player A. (c) In the gambler's ruin problem in part (b), how many rounds is the game expected to last

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