Problem 2. (Diagonal Entry in Wishart Random Matrix) For px p random matrix M ~ W(,...

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Problem 2. (Diagonal Entry in Wishart Random Matrix) For px p random matrix M ~ W₂(Σ, m), prove the following results. 1) Show that, for any constant vector a ‡ 0, we have: a'Ma a' Ea ~ Xm i=1 Hint: Note that M = ₁ Z₁Z, where Z₁,..., Zm are i.i.d multivariate normal random vector. For any vector a, we can write a'Ma = a'Σ¹/²(Σ-¹/²MΣ-¹/²)Σ¹/²a. Problem 2. (Diagonal Entry in Wishart Random Matrix) For px p random matrix M ~ W₂(Σ, m), prove the following results. 1) Show that, for any constant vector a ‡ 0, we have: a'Ma a' Ea ~ Xm i=1 Hint: Note that M = ₁ Z₁Z, where Z₁,..., Zm are i.i.d multivariate normal random vector. For any vector a, we can write a'Ma = a'Σ¹/²(Σ-¹/²MΣ-¹/²)Σ¹/²a.

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5019 M m 9px 0 costant vector By definition of mishart dist It M ou lalp 5 m m Then M ... View the full answer