Part BCSIR NET June 2025the-marginal-correlation-is-one-half-and-all-of-it-is-the-shared-x

The marginal correlation is one half and all of it is the shared x

Suppose $(X_{1}, X_{2}, X_{3})^{T}$ ~ $N_{3} (0, I_{3})$ , where 0 is the zero mean vector and $I_{3}$ is the 3 × 3 identity matrix, and $(X, Y, Z)^{T} = A (X_{1}, X_{2}, X_{3})^{T}$ where A has rows (3, 0, 0), (2, 2, 0) and (4, 0, 4). Then the partial correlation coefficient $ρ_{Y Z . X}$ is

A.1/2
B.2/3
C.3/4
D.0✓

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 dependence misread.

See pricing

50 are analysed free — try those first.

The trap it tests

Dependence misread

Independence, pairwise vs mutual, or correlation vs dependence.

Drill statements like this

The marginal correlation is one half and all of it is the shared x

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