Let X1,X2,…,X25 be a random sample of size 25 from a population having N3(mu, Sigma) distribution, where mu and non-singular Sigma are unknown parameters. Let S = 1/24 sumj=1^25 (Xj - barX)(Xj - barX)^T, where barX = 1/25 sumj=1^25 Xj, and B = beginpmatrix1 & 2 & 3 -1 & 0 & 1endpmatrix. Then which one of the following statements is true?

(C) 24 B S B^T follows a Wishart distribution of order 2 with 24 degrees of freedom

Q45Section ST (Statistics (Q11–Q65))45 of 65

Wishart law of a quadratic form

Let $\mathbf{X}_1,\mathbf{X}_2,…,\mathbf{X}_{25}$ be a random sample of size 25 from a population having $N_3(\boldsymbol{\mu}, \Sigma)$ distribution, where $\boldsymbol{\mu}$ and non-singular $\Sigma$ are unknown parameters. Let $S = \frac{1}{24} \sum_{j=1}^{25} (\mathbf{X}_j - \bar{\mathbf{X}})(\mathbf{X}_j - \bar{\mathbf{X}})^T$ , where $\bar{\mathbf{X}} = \frac{1}{25} \sum_{j=1}^{25} \mathbf{X}_j$ , and $B = \begin{pmatrix}1 & 2 & 3 \ -1 & 0 & 1\end{pmatrix}$ . Then which one of the following statements is true?

Pick an option to check your answer. In a mock test a wrong answer here costs 2/3 mark.

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