GATE 2020 ST – Question 59
Four iid observations come from a continuous symmetric location density fθ(x)=f(x−θ), with f(−x)=f(x). Under H₀:θ=0, let T⁺ be the Wilcoxon positive signed-rank sum. Find32P(T⁺≤5).
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Correct answer: 18 to 18
Explanation
Under the null each subset of ranks{1,2,3,4} is the positive-sign subset with probability1/16. Subsets of sum≤5 are∅,{1},{2},{3},{4},{1,2},{1,3},{1,4},{2,3}:nine outcomes. Thus probability9/16 and32 times it equals18. Continuity avoids tied or zero ranks.