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3. Consider a clock with marks 1, 2, ..., 6. The movement of minute and hour hand are independent. The minute hand moves one step clockwise with rate a, one step coun- terclockwise with rate . The hour hand moves one step clockwise with rate y, and counterclockwise with rate 8. (a) Find the asymptotic portion of time of which the two hands overlapped. (Hint: consider the difference of marks, mod 6.) (b) Set (a,b, 7, 8) = (1, 2, 3, 4). Suppose at time t = 0 the minute and hour hand are at Mark 3,6. Let T be the first time when the two hands are overlapped. Find E[T]. 3. Consider a clock with marks 1, 2, ..., 6. The movement of minute and hour hand are independent. The minute hand moves one step clockwise with rate a, one step coun- terclockwise with rate . The hour hand moves one step clockwise with rate y, and counterclockwise with rate 8. (a) Find the asymptotic portion of time of which the two hands overlapped. (Hint: consider the difference of marks, mod 6.) (b) Set (a,b, 7, 8) = (1, 2, 3, 4). Suppose at time t = 0 the minute and hour hand are at Mark 3,6. Let T be the first time when the two hands are overlapped. Find E[T]