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(4.3) An experiment consists of firing a projectile at a target and observing the posi- tion of the point of impact. (Su
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(4.3) An experiment consists of firing a projectile at a target and observing the posi- tion of the point of impact. (Suppose the origin of the coordinate system is placed at the target.) Then, an outcome is a pair w-6,02), where w, is the abscissa and W, the ordinate of the point of impact. The sample space 2 consists of all such pairs 6. For each w € 12, let X(0) -10.1. Y(0) -6.1. Z(0) - + 18 PROBABILITY SPACES AND RANDOM VARIABLES Chap. 1 (a) What do X, Y, Z stand for? (b) Suppose the probability measure P is such that P(lo : 0,50,63 Sb) - | | __exp[-Ź («* +9x)] dx dy. Then show that X and Y are independent random variables with the same distribu- tion function 1 (1) 0) - S -*'2dx, OSI<oo.