Hw6-ORIE3510_S12

# Hw6-ORIE3510_S12 - ORIE 3510 Homework 6 Instructor: Mark E....

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

ORIE 3510 – Homework 6 Instructor: Mark E. Lewis due Wednesday March 9, 2012 (ORIE Hallway drop box) 1. One light bulb at Rhodes student lounge has a maximum life of m days. In each day, the bulb will go crashed with probability p , in which case a new bulb must be installed to replace the broken one. Also a bulb that has survived for m days must be replaced regardless of whether it is still working or not. In the long run, what is the fraction of time that a student will ﬁnd a newly-installed fresh light bulb in the lounge? 2. Consider a discrete Markov chain with transition matrix P = 0 1 2 3 0 . 1 0 . 3 0 . 3 0 . 3 0 . 1 0 . 1 0 . 5 0 . 3 0 . 3 0 . 2 0 . 1 0 . 4 0 . 3 0 . 3 0 . 3 0 . 1 Suppose that the chain initially starts randomly with equal probabilities in one of the 4 states. (a) What is the probability that state 0 is visited before state 3? (b) What is the expected waiting time until state 0 is visited for the ﬁrst time? (c) What is the expected time between two visits to state 0?

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.

## This note was uploaded on 03/08/2012 for the course OR&IE 3510 taught by Professor Lewis during the Spring '10 term at Cornell University (Engineering School).

### Page1 / 2

Hw6-ORIE3510_S12 - ORIE 3510 Homework 6 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