Mathematics · Statistics and Probability

Let (X1, X2, ..., X7) and (Y1, Y2, ..., Y9) be two independent random samples from continuous distribution functions F(x - μ) and F(x - θ) respectively, where F, μ, and θ are unknown. Let Ri be the rank of Yi in the combined sample of size 16, for i = 1, 2, ..., 9. For testing H0: μ = θ against H1: μ > θ, the Wilcoxon rank sum test statistic T = ∑i=19 Ri is proposed. Under H0, what is the expected value E(T)?