Homework9 - ST561 Fall 2010 Homework 9 Due Monday Nov 29th...

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ST561 Fall 2010 Homework 9 Due: Monday, Nov. 29th, 2010 1. Let X = ( X 1 , . . . , X p ) T follow a multivariate normal distribution with mean μ and covariance matrix Σ. That is X MV N ( μ , Σ) with joint pdf f X ( x ) = 1 (2 π ) p/ 2 | Σ | 1 / 2 exp ' - ( x - μ ) T Σ - 1 ( x - μ ) / 2 where | Σ | is the determinant of Σ. Let Y = A X , where A is a p × p matrix with its inverse A - 1 exists. Use the method of transformation, show that Y MV N ( A μ , A Σ A T ). 2. Let Z = ( Z 1 , . . . , Z
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Unformatted text preview: ) T with { Z i } p i =1 being i.i.d. N (0 , 1). For any given positive definite p × p matrix Σ, using the result from (1), find a transform matrix A such that Y = A Z follows a multivariate normal with mean μ = (0 ,..., 0) T and covariance Σ. 3. Textbook page 233, 4.4.8. 4. Textbook Page 233, 4.4.10. 1...
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