Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Random Variables & Distribution Functions
For n ≥ p +1, let \(\underline{X_1}, \underline{X_2}, \ldots, \underline{X_n}\) be a random sample from \(N_p(\underline{\mu}, \Sigma), \underline{\mu} \in \mathbb{R}^p\) and Σ is a positive definite matrix. Define \(\underline{\bar{X}}=\frac{1}{n} \sum_{i=1}^n \underline{X_i}\) and \(A=\sum_{i=1}^n(\underline{X_i}-\underline{\bar{X}})(\underline{X_i}-\underline{\bar{X}})^T\). Then the distribution of Trace(AΣ-1) is
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Wp(n - 1, Σ)
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\(\chi_p^2\)
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\(\chi_{n p}^2\)
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χ2(n - 1)p