Mathematics · Nonparametric Statistics

Let (X1, Y1), …, (X4, Y4) be a random sample from a continuous bivariate distribution function FX,Y with marginal distributions of X and Y being FX and FY respectively. In order to test the null hypothesis H0: 'X and Y are independen t' against the alternative H1: 'X and Y are positively associated', consider the Kendall sample correlation statistic: K = ∑i=13 ∑j=i+14 ψ((Xi, Yi), (Xj, Yj)) where ψ((a, b), (c, d)) = 1 if (d−b)(c−a) > 0, and −1 if (d−b)(c−a) < 0. Assuming no ties, which of the following statements is true?