{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ex3soln - ECE320 Solutions to Third Examination Spring 2006...

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

View Full Document Right Arrow Icon
ECE320 Solutions to Third Examination Spring 2006 Cornell University T.L.Fine 1. A finite state system with certain random inputs moves between its states such that its motion can be described by a Markov chain with the one-step transition probability matrix P = . 6 . 4 0 0 0 0 . 9 . 1 0 0 0 0 . 5 . 5 0 0 0 . 6 . 4 0 0 0 0 0 1 . (a)(3pts) Sketch a state transition diagram for P . See Figure 1. 1 2 3 4 5 1 .4 .6 .1 .9 .5 .5 .4 .6 Figure 1: (b)(5pts) Identify all communicating classes of states and determine whether they are open or closed. C 1 = { 1 } , open C 2 = { 2 } , open C 3 = { 3 , 4 } , closed C 4 = { 5 } , closed. 1
Image of page 1

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

View Full Document Right Arrow Icon
(c)(4pts) If the Markov chain state X 1 is equally probable to occupy any of its states, what are the probabilities for state occupancies of X 2 ? The probabilities π (2) = π (1) P = [ . 2 . 2 . 2 . 2 . 2] P = 1 5 [ . 6 1 . 3 1 . 2 . 9 1] . (d)(3pts) If the Markov chain starts with X 1 = 3, what are the long-run probabilities of the chain occupying its states? If we start in state 3 then we remain in the closed class C 3 = { 3 , 4 } . The one-step transition matrix for
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern