Between two distinct methods for manufacturing certain goods, the quality of goods produce...

Between two distinct methods for manufacturing certain goods, the quality of goods produced by method i is a continuous random variable having distribution Fi , i = 1,2. Suppose that n goods are produced by method 1 and m by method 2. Rank the n + m goods according to quality, and let

For the vector X1, X2,... ,Xn+m, which consists of n l’s and m 2’s, let R denote the number of runs of 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 distributed goods), what arc the mean and variance of R?