33. 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 Ui and Di be the events that the price of the stock moves up and down on the ith trading day, respectively. In terms of Ui’s and Di’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.