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Q22Section ST (Statistics (Q11–Q65))22 of 65

Concordance probability for independent pairs

Let (X1,Y1),(X2,Y2),…,(Xn,Yn)(X_1, Y_1), (X_2, Y_2), \dots, (X_n, Y_n), n≥2n \ge 2, be a random sample from a continuous bivariate distribution with joint distribution function FX,YF_{X,Y}. Further, FXF_X and FYF_Y are the marginal distribution functions of XX and YY, respectively. If FX,Y(x,y)=FX(x)FY(y)F_{X,Y}(x, y) = F_X(x)F_Y(y) for all (x,y)(x, y), then, for any two independent pairs (Xi,Yi)(X_i, Y_i) and (Xj,Yj)(X_j, Y_j), P[(Xi−Xj)(Yi−Yj)>0]P[(X_i - X_j)(Y_i - Y_j) > 0] equals

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