Part CCSIR NET December 2023spearman-for-bivariate-normal

Spearman for bivariate normal

Let $(X_{1}, Y_{1}), (X_{2}, Y_{2}), (X_{3}, Y_{3})$ be i.i.d. bivariate normal with mean (0, 0) and correlation matrix $[[1, \rho], [\rho, 1]]$ , | $\rho$ | < 1. Let $S_\rho = 3E($ sgn $(X_{1} - X_{2})(Y_{1} - Y_{3}))$ . Which of the following statements are true?

A.If $X_{1}$ and $Y_{1}$ are independent, then $S_\rho = 0$ ✓ Correct
B. $S_\rho = (6/\pi) \sin$ ⁻ $^{1}(\rho/2)$ ✓ Correct
C.If $S_\rho = 0$ , then $X_{1}$ and $Y_{1}$ are independent✓ Correct
D.If $X_{1}$ and $Y_{1}$ are independent, then $S_\rho = 1/2$

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, and why this one tests hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Spearman for bivariate normal

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