40. There are two distinct methods for manufacturing certain goods, the quality of goods produced by method
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40. There are two distinct methods for manufacturing certain goods, the quality of goods produced by method i being a continuous random variable having distribution F,, i = 1, 2. Suppose that a goods are produced by method 1 and m by method 2. Rank the n+m goods according to quality and let x=2 if the ith best was produced from method 1 otherwise 1, For the vector X1, X2, Xn which consists of a l's and m 2's, let R denote the number of runs of 1. For instance, if n 5, m2, and X 2, 1, 1, 1, 1, 2, then R 2. If F₁ F2 (that is, if the two methods produce identically distributed goods), what are the mean and variance of R?
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