My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum

LinkBack Thread Tools Display Modes
July 7th, 2014, 07:32 AM   #1
Joined: Jun 2014
From: SriLanka

Posts: 5
Thanks: 0

Do you know Markov chain?

A particle moves on a circle through points which have been marked 0, 1, 2, 3, 4 (in a clockwise
order). At each step it has a probability p of moving to right (clock-wise) and (1-p) to the left
(counter-clock wise). Let X n denote its location on the circle after the nth step.
(i) Explain why {X n , n ≥ 0} is a Markov chain.
(ii) Find the transition probability matrix.

Please Help me..
Hemantha is offline  
July 7th, 2014, 12:57 PM   #2
Global Moderator
Joined: May 2007

Posts: 6,807
Thanks: 717

{i} Essentially by definition. The distribution of X(n+1) depends entirely on the value of X(n).
(ii) (I forgot the exact form of a transition matrix). Each row should look like (1-p),0,p,0,0 rotated. First row p in second column, second row p in third column, etc. (I may have rows and columns interchanged).
mathman is offline  

  My Math Forum > High School Math Forum > Probability and Statistics

chain, markov

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Help with Hidden Markov chain dr_romix Advanced Statistics 2 October 16th, 2012 06:36 PM
help in markov chain legendoulis Advanced Statistics 4 April 4th, 2012 11:28 AM
Markov Chain problem 450081592 Advanced Statistics 1 March 6th, 2012 04:17 PM
Markov chain butabi Advanced Statistics 1 February 12th, 2012 03:20 PM
Markov Chain matrix Turloughmack Linear Algebra 0 February 7th, 2011 05:15 AM

Copyright © 2019 My Math Forum. All rights reserved.