Let X 1 and X 2 be two i.i.d. p × 1 multivariate normal random vectors with mean μ and positive definite dispersion matrix Σ. Then which of the following random variables always has a central chi-square distribution?

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Mathematics · Statistics

Let X 1 and X 2 be two i.i.d. p × 1 multivariate normal random vectors with mean μ and positive definite dispersion matrix Σ. Then which of the following random variables always has a central chi-square distribution?

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1 2 (X 1 - X 2 ) T Σ -1 (X 1 - X 2 )

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Answer 1

1 2 (X 1 - X 2 ) T Σ -1 (X 1 - X 2 )

Answer 2

2(X 1 - X 2 ) T Σ -1 (X 1 - X 2 )

Answer 3

2(X 1 - X 2 ) T (X 1 - X 2 )

Answer 4

1 2 (X 1 - X 2 ) T (X 1 - X 2 )

Let X 1 and X 2 be two i.i.d. p × 1 multivariate normal random vectors with mean μ and positive definite dispersion matrix Σ. Then which of the following random variables always has a central chi-square distribution?

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Let X 1 and X 2 be two i.i.d. p &times; 1 multivariate normal random vectors with mean &mu; and positive definite dispersion matrix &Sigma;. Then which of the following random variables always has a central chi-square distribution?

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Let X 1 and X 2 be two i.i.d. p × 1 multivariate normal random vectors with mean μ and positive definite dispersion matrix Σ. Then which of the following random variables always has a central chi-square distribution?