Part BCSIR NET December 2023wishart-trace

Wishart trace

For n ≥ p + 1, let $X_{1}, \dots, X_{n}$ be a random sample from $N_{p} (μ, \sum)$ with $\sum$ positive definite. Define X̄ and $A = \sum (X_{i} - \overset{ˉ}{X}) (X_{i} - \overset{ˉ}{X})^{T}$ . The distribution of Trace $(A \sum$ ⁻ $^{1})$ is

A. $W_{p} (n - 1, \sum)$
B. $χ_{p}^{2}$
C. $χ_{n p}^{2}$
D. $χ_{(n - 1) p}^{2}$

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Wishart trace

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