STAT_333_Assignment_3

STAT_333_Assignment_3 - STAT 333 Assignment 3 Due: Tuesday,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 333 Assignment 3 Due: Tuesday, July 27 at the beginning of class 1. Consider a discrete-time Markov Chain with state space S = {0, …, 7} and transition matrix P = 1/2 1/4 0 0 0 0 1/4 0 1/4 0 0 0 0 0 3/4 0 0 0 1/3 0 0 0 0 2/3 0 1/5 1/5 1/5 1/5 1/5 0 0 1/6 0 0 0 1/3 1/6 1/6 1/6 0 0 0 0 0 1 0 0 1/4 0 0 0 0 0 3/4 0 0 0 2/3 0 0 0 0 1/3 a. Determine the classes of this chain, which are open or closed, write P in simplified form, and find the period of each closed class. b. Find the equilibrium distribution corresponding to each closed class. Write down the general form of all stationary distributions for this chain. c. Find the absorption probabilities from each transient state into each closed class. d. Describe the long-run behaviour of the chain if X 0 = 0. Do the same if X 0 = 3. 2. NOTE: You may use mathematical software for this question, just include your output. Consider a discrete-time Markov Chain with five transient states (1, 2, 3, 4, and 5) and two recurrent states (6 and 7). The chain is equally likely to start in any of the transient P = 1/2 0 1/4 0 0 0 1/4 0 1/3 0 1/3 0 1/3 0 1/5 1/5 1/5 1/5 1/5 0 0 0 0 0 1/4 1/4 1/4 1/4 2/3 0 1/3 0 0 0 0 0 0 0 0 0 1/2 1/2 0 0 0 0 0 1/3 2/3 states. The transition matrix is
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/12/2010 for the course STAT 333 taught by Professor Chisholm during the Spring '08 term at Waterloo.

Page1 / 2

STAT_333_Assignment_3 - STAT 333 Assignment 3 Due: Tuesday,...

This preview shows document pages 1 - 2. Sign up to view the full document.

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