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Suppose that each day the price of a stock moves up 1/8 of a point, moves down 1/8 of a point, or remains unchanged. For i ≥ 1, let U_{i} and Di be the events that the price of the stock moves up and down on the ith trading day, respectively. In terms of U_{i}’s and D_{i}’s, find an expression for the event that the price of the stock
(a) remains unchanged on the ith trading day;
(b) moves up every day of the next n trading days;
(c) remains unchanged on at least one of the next n trading days;
(d) is the same as today after three trading days;
(e) does not move down on any of the next n trading days.
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