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Part CCSIR NET December 2023wishart-quadratic-forms

Wishart quadratic forms

Suppose $A = (a_{ij})$ ~ $W_{3} (5, \sum)$ , where $\sum = [[2, 1, 1], [1, 2, 0], [1, 0, 2]]$ . Then which of the following statements are true?

A. $a_{22}$ ~ $χ_{3}^{2}$
B.½ $a_{22}$ ~ $χ_{5}^{2}$
C. $(1/33) (a_{11} - 4 a_{13} + 4 a_{33})$ ~ $χ_{3}^{2}$
D. $(1/9) (a_{11} - 4 a_{13} + 4 a_{33})$ ~ $χ_{5}^{2}$

The answer and working come with the PYQ pack.

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The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: If every marginal is normal then the vector is multivariate normal

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