Between two distinct methods for manufacturingcertain
Chapter 7, Problem 7.44(choose chapter or problem)
Between two distinct methods for manufacturingcertain goods, the quality of goods produced bymethod i is a continuous random variable havingdistribution Fi, i = 1, 2. Suppose that n goods areproduced by method 1 and m by method 2. Rankthe n + m goods according to quality, and letXj =1 ifthejth best was produced frommethod 12 otherwiseFor the vector X1,X2, . . . ,Xn+m, which consists ofn 1s and m 2s, let R denote the number of runsof 1. For instance, if n = 5,m = 2, and X =1, 2, 1, 1, 1, 1, 2, then R = 2. If F1 = F2 (that is,if the two methods produce identically distributedgoods), what are the mean and variance of R?
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