{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

homework2 2010 solutions

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

This preview shows pages 1–3. Sign up to view the full content.

ECN/APEC 7240 Spring 2010 Homework 2 Solutions 1) a) Denote the transition matrix . 1 1 ] | Pr[ ] | Pr[ ] | Pr[ ] | Pr[ 1 1 1 1 - - = = = = = = = = = = Π + + + + p p p p h t h t h t l t l t h t l t l t τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ 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 . 0 1 1 = - - - - = - Π λ λ λ p p p p I 0 ) 1 ( 2 2 = - - - p p λ 0 ) 1 ( 2 ) 1 ( 2 = - - - λ λ p 0 ) 2 1 )( 1 ( = - - - λ λ 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 0 0 1 1 1 1 1 1 1 1 1 2 1 I PP T = = - - =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ECN/APEC 7240 Spring 2010 Meanwhile , 2 1 0 0 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 - = - - - = - - - - = Π = Λ p p p p p p p P P T which is a diagonal matrix. Clearly .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern