Hw4-ORIE3510_S12

# Hw4-ORIE3510_S12 - ORIE 3510 Homework 4 Instructor Mark E...

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

ORIE 3510 – Homework 4 Instructor: Mark E. Lewis due 2PM, Wednesday February 22, 2012 (ORIE Hallway drop box) 1. Show that if state i is recurrent and state i does not communicate with state j , then p ij = 0. (This implies that once a process enters a recurrent class of states, it can never leave that class. For this reason, a recurrent class is often referred to as a closed class). 2. Consider a Markov chain with state space S = { 1 , 2 ,..., 9 } and transition matrix given by 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 / 2 0 0 0 1 / 2 0 0 0 0 1 / 2 0 0 0 1 / 2 0 0 0 0 0 0 0 0 0 2 / 3 1 / 3 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 / 4 0 3 / 4 0 0 0 0 0 0 0 1 0 0 0 a) Classify the states. b) Which classes are transient? Which classes are recurrent? c) What are the periods of each state? 3. A transition probability matrix P is said to be doubly stochastic if the sum over each column equals one; that is X i p ij = 1 for all j If such a chain is irreducible and aperiodic and consists of

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Hw4-ORIE3510_S12 - ORIE 3510 Homework 4 Instructor Mark E...

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

View Full Document
Ask a homework question - tutors are online