1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statistics - Discrete Markov Chains

  1. Apr 30, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution

    I'm not really sure if this belongs here or in the precalculus mathematics section. I had to take calculus before taking this class so I'm putting it here.

    I'm confused about part (b). I don't really understand how I'm supposed to find [itex]P(X_{n+2}=0|X_{n}=2)[/itex] because I don't know what state n+1 is. Thanks for any help.
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 30, 2013 #2
  4. Apr 30, 2013 #3
    [itex]P(X_{n+2}=0) = P(X_{n+2}=0|X_{n}=2)P(X_{n}=2) + P(X_{n+2}=0|X_{n}=1)P(X_{n}=1) + P(X_{n+2}=0|X_{n}=0)P(X_{n}=0)[/itex]
    [itex]P(X_{n+2}=0|X_{n}=2)P(X_{n}=2) = P(X_{n+2}=0) - P(X_{n+2}=0|X_{n}=1)P(X_{n}=1) - P(X_{n+2}=0|X_{n}=0)P(X_{n}=0)[/itex]

    I'm not sure how this helps.
  5. Apr 30, 2013 #4
    You're using the wrong events.

    Do this

    P(X_{n+2} = 0~\vert~X_n=2)
    & = & P(X_{n+2} = 0~\vert~X_n=2,~X_{n+1}=0)P(X_{n+1}=0~\vert~X_n=2)\\
    & & + P(X_{n+2} = 0~\vert~X_n=2,~X_{n+1}=1)P(X_{n+1}=1~\vert~X_n=2)\\
    & & + P(X_{n+2} = 0~\vert~X_n=2,~X_{n+1}=2)P(X_{n+1}=2~\vert~X_n=2)
  6. Apr 30, 2013 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    If you had been told that ##X_0 = 2## would you have been able to work out the probability that ##X_2 = 0?## Have you really never seen how to get multi-step transition probabilities?

    Note: I am waiting for answers to these questions before offering more help.
    Last edited by a moderator: May 6, 2017
  7. May 2, 2013 #6
    Well for b) I got .21 and believed that I solved the problem correctly. I don't know exactly what c is even asking me. Find P(X_1 = 0). What exactly are the alphas? Like what do they represent? Alpha 1 = probability x equals zero is .25.

    I have indeed never seen how to get multi-step transition probabilities =( but i believe i figured it out correctly and got the answer.

    Thanks for your help guys.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted