For 25 iid N₃(μ,Σ) observations,Σ nonsingular, let S=Σⱼ₌₁²⁵(X_j−X̄)(X_j−X̄)ᵀ/24 and $B=\begin{pmatrix}1&2&3\\-1&0&1\end{pmatrix}$. Which describes 24BSBᵀ?
Correct answer: (C) Wishart of order 2,24 degrees of freedom
Explanation
The sample scatter 24S~W₃(Σ,24). Under the rank-two linear transform B, B(24S)Bᵀ~W₂(BΣBᵀ,24). Order equals the transformed vector dimension 2, and centering uses one sample degree of freedom, leaving 24. **C**.
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