STAT230 Study Guide - Midterm Guide: Joint Probability Distribution, Fair Coin, Talking Lifestyle 1278
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In a quality control inspection items are classi ed as having a minor defect, a major defect, or as being acceptable. A carton of 10 items contains 2 with minor defects, 1 with a major defect, and 7 acceptable. Three items are chosen at random from the carton without replacement. Let x be the number selected with minor defects and y be the number with major defects. [2] (a) find the joint probability function f (x, y) of (x, y ). (cid:16)2 x f (x, y) = (cid:17)(cid:16)1 (cid:17)(cid:16) 7 (cid:16)10 (cid:17) y. 3 x y (cid:17) x = 0, 1, 2 , y = 0, 1 . [2] (b) find the marginal probability function of x. The marginal probability is hypergeometric: (cid:16)2 (cid:17) x = 0, 1, 2 . (cid:17)(cid:16) 8 (cid:16)10 (cid:17) 3 (c) find the probability p (x = 1 | y = 0). P (x = 1 | y = 0) = f (1, 0) f2(0)