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Part BCSIR NET December 2023wishart-trace

Wishart trace

For n ≥ p + 1, let X1,…,XnX_{1}, \dots, X_{n} be a random sample from Np(μ,∑)N_{p}(\mu, \sum) with ∑\sum positive definite. Define X̄ and A=∑(Xi−Xˉ)(Xi−Xˉ)TA = \sum(X_{i} - {\bar{X}})(X_{i} - {\bar{X}})^{T}. The distribution of Trace(A∑(A\sum⁻1)^{1}) is

  1. A.Wp(n−1,∑)W_{p}(n - 1, \sum)
  2. B.χp2\chi^{2}_{p}
  3. C.χnp2\chi^{2}_{np}
  4. D.χ(n−1)p2\chi^{2}_{(n-1)p}✓ Correct

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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