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Let {P(µ,Σ) : µ ∈ R^k, Σ ∈ M_k} be a location-scale family on R^k. Suppose that P(0,I_k) has a Lebesgue p.d.f. that is always positive and that the mean and variance-covariance matrix of P(0,Ik) are 0 and Ik, respectively. Show that the mean and variance-covariance matrix of P(µ,Σ) are µ and Σ, respectively.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
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