Let X1 and X2 be two independent continuous random variables. Define and S-Ixpo+2xso) where Ry and...

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Let X1 and X2 be two independent continuous random variables. Define and S-Ixpo+2xso) where Ry and R2 are the Wilcoxon signed ranks of X, and X2, respectively. (a) Assume that X, and X2 have symmetric distributions about 0. Show that Pr(T ) Pr(S-t) for 0,1,2,3 using the properties of symmetry:-Xi ~ x, and Pr(X, > 0)-Pr(X, <0) = 0.5 (b) Suppose that X1 and X2 are identically distributed with common density -05%:- 10.5sx <0 0.5 0sxs1 show that Pr(T+-): Pr(S = 1).

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Let X1 and X2 be two independent continuous random variables. Define and S-Ixpo+2xso) where Ry and...

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