Part CCSIR NET December 2024one-value-of-the-statistic-arises-twice

One value of the statistic arises twice

Let $X_{1}, X_{2}, X_{3}$ be a random sample of size 3 from an absolutely continuous distribution that is symmetric about 0. For i = 1, 2, 3, let $R_{i}$ denote the rank of | $X_{i}$ | among | $X_{1}$ |, | $X_{2}$ | and | $X_{3}$ |. If T⁺ $= \sum (i : X_{i} > 0) R_{i}$ is the Wilcoxon signed-rank statistic, then which of the following statements are true?

A.P(T⁺ = 3) = 1/4✓
B.Var(T⁺) = 7/2✓
C.P(T⁺ > 3) = 5/8
D.P(T⁺ > 4) = 1/8

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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One value of the statistic arises twice

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