Part BCSIR NET December 2024the-schur-complement-loses-one-degree-of-freedom

The schur complement loses one degree of freedom

Let X, Y and Z be random variables such that S = [[X, Y], [Y, Z]] ~ $W_{2} (10, \sum)$ , where $W_{2}$ denotes the Wishart distribution and $\sum = [[1, 1/2], [1/2, 1]]$ . Define $T = Z - Y^{2} / X$ . Then, Var(T) equals

A.77/6
B.81/8✓
C.83/9
D.79/7

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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The schur complement loses one degree of freedom

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