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Part CCSIR NET December 2023wishart-quadratic-forms

Wishart quadratic forms

Suppose A=(aij)A = (a_{ij}) ~ W3(5,∑)W_{3}(5, \sum), where ∑=[[2,1,1],[1,2,0],[1,0,2]]\sum = [[2, 1, 1], [1, 2, 0], [1, 0, 2]]. Then which of the following statements are true?

  1. A.a22a_{22} ~ χ32\chi^{2}_{3}
  2. B.½ a22a_{22} ~ χ52\chi^{2}_{5}✓ Correct
  3. C.(1/33)(a11−4a13+4a33)(1/33)(a_{11} - 4a_{13} + 4a_{33}) ~ χ32\chi^{2}_{3}
  4. D.(1/9)(a11−4a13+4a33)(1/9)(a_{11} - 4a_{13} + 4a_{33}) ~ χ52\chi^{2}_{5}

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 execution slip.

See pricing

50 are analysed free — try those first.

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

More on this topic

The chapter behind this: Multivariate normal and Wishart — free to read

From Linear Models and Multivariate › Multivariate normal distribution

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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