hA - Stat 5101 (Geyer) Fall 2011 Homework Assignment 10 Due...

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Stat 5101 (Geyer) Fall 2011 Homework Assignment 10 Due Wednesday, November 30, 2011 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 10-1. Suppose ( X 1 ,X 2 ) is a bivariate normal random vector, and assume it is nondegenerate. Write its PDF in terms of the mean vector and variance matrix. Then rewrite its PDF in terms of new parameters, which are E ( X 1 ) = μ 1 E ( X 2 ) = μ 2 sd( X 1 ) = σ 1 sd( X 2 ) = σ 2 cov( X 1 ,X 2 ) = ρσ 1 σ 2 Then simplify your expression for the PDF so it contains no matrices, no matrix inverses, determinants, or matrix multiplication. Hint: the inverse of a matrix A = ± a 11 a 12 a 21 a 22 ² can be done by Cramer’s rule obtaining A - 1 = 1 det( A ) ± a 22 - a 12 - a 21 a 11 ² assuming A is invertible, which it is if det( A ) is not zero. 10-2. Suppose ( X 1 ,X 2 ) is a nondegenerate bivariate normal random vec- tor. Calculate the conditional PDF of

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This note was uploaded on 09/13/2011 for the course STA 4184 taught by Professor Staff during the Spring '11 term at University of Central Florida.

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hA - Stat 5101 (Geyer) Fall 2011 Homework Assignment 10 Due...

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