Let X be a p × p matrix-valued random variable having the Wishart distribution with parameters Σ (covariance matrix) and m (degrees of freedom). Which of the following statements is necessarily true?

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Mathematics · Probability and Statistics

Let X be a p × p matrix-valued random variable having the Wishart distribution with parameters Σ (covariance matrix) and m (degrees of freedom). Which of the following statements is necessarily true?

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Option C

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Answer 1

Any k × k submatrix of X also has a Wishart distribution for k < p

Answer 2

c X 1,1 has a Chi-square distribution with m - p + 1 degrees of freedom for a suitable constant c

Answer 3

c X 1,2 has a Chi-square distribution with m - p + 1 degrees of freedom for a suitable constant c

Let X be a p × p matrix-valued random variable having the Wishart distribution with parameters Σ (covariance matrix) and m (degrees of freedom). Which of the following statements is necessarily true?

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Let X be a p &times; p matrix-valued random variable having the Wishart distribution with parameters &Sigma; (covariance matrix) and m (degrees of freedom). Which of the following statements is necessarily true?

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Let X be a p × p matrix-valued random variable having the Wishart distribution with parameters Σ (covariance matrix) and m (degrees of freedom). Which of the following statements is necessarily true?