homework2 2010 solutions

homework2 2010 solutions - ECN/APEC 7240 Spring 2010...

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Unformatted text preview: ECN/APEC 7240 Spring 2010 Homework 2 Solutions 1) a) Denote the transition matrix . 1 1 ] | Pr[ ] | Pr[ ] | Pr[ ] | Pr[ 1 1 1 1 -- = = = = = = = = = = + + + + p p p p h t h t h t l t l t h t l t l t One way to compute the powers of a matrix is to diagonalize it by finding the eigenvalues of the matrix. These solve the characteristic equation . 1 1 =---- =- p p p p I ) 1 ( 2 2 =--- p p ) 1 ( 2 ) 1 ( 2 =--- p ) 2 1 )( 1 ( =--- p Thus the eigenvalues are 1 and 1 - 2 p . The corresponding eigenvectors are (1, 1) and (1, - 1) since = -- 1 1 1 1 1 1 p p p p . 1 1 ) 2 1 ( 1 2 2 1 1 1 1 1 -- = -- = - -- p p p p p p p Note that - = 1 1 1 1 2 1 P is an orthogonal matrix such that . 1 1 1 1 1 1 1 1 1 1 2 1 I PP T = = - - = ECN/APEC 7240 Spring 2010 Meanwhile , 2 1 1 1 2 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 - = -- - = - -- - = = p p p p p p p P P T which is a diagonal matrix. which is a diagonal matrix....
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.

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homework2 2010 solutions - ECN/APEC 7240 Spring 2010...

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