stats150-6 - STAT 150 FINAL -SPRING 2007 Instructor: Steven...

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

View Full Document Right Arrow Icon
Sheet1 Page 1 STAT 150 FINAL -SPRING 2007 Instructor: Steven Evans Instructions: Each question is worth an equal amount. Explain carefully and completely what you are doing at each step in full s Quote any results that you use from class. NAME: SID: 1) 2) 3) 4) 5) 6) TOTAL 1) Let p be a probability distribution on the nonnegative integers such that i > 0 for all i. Write down the transition matrix of an irreducible, aperiodic, recurrent Markov chain on the nonnegative integers that has p as stationary probability distribution. s 2) Consider the Markov chain with the following transition matrix . . 00.50 0 00.5 0.25 0 0.25 0.25 0 0.25 00.500.50 0 0 0.25 0.25 0 0.25 0.25 0 0 0 0.5 0 0.5 0.25 0.25 0 0.25 0.25 0 BBBBB CCCCC
Background image of page 1

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

View Full DocumentRight Arrow Icon
Sheet1 Page 2 P = Show that this chain is irreducible and aperiodic, and find the stationary probability distribution of the chain by showing that th e is reversible. i 3) Consider a Yule process with immigration. This is a birth-and-death
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/11/2009 for the course CEE cee taught by Professor Monteiro during the Fall '05 term at University of California, Berkeley.

Page1 / 3

stats150-6 - STAT 150 FINAL -SPRING 2007 Instructor: Steven...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online