The loose minute hand of a clock is spun hard. The coordinates (x, y) of the point where the tip of the hand comes to rest is noted. Z is defined as the sgn function of the product of x and y, where sgn(t) is 1 if if and if (a) Describe the underlying space S of this random experiment and specify the probabilities of its events. (b) Show the mapping from S to the range of X. (c) Find the probabilities for the various values of X