November 18th, 2009, 12:07 PM  #1 
Newbie Joined: Sep 2009 Posts: 18 Thanks: 0  Markov Chains
Hi, I am understanding Markov chains for the most part. However, this problem I am struggling with I need to know how to derive the transition matrix. A red urn contains 2 red marbles and 3 blue marbles,and a blue urn contains 1 red marble and 4 blue marbles. A marble is selected from an urn, the color is noted, and the marble is returned to the urn from which it was drawn. The next marble is drawn from the urn whose color is the same as the marble just drawn. The only question I need help with is deriving the transition matrix. The matrix is : .4 .6 .2 .8 
November 18th, 2009, 01:55 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
Are you saying you haven't noticed that each element is a probability of a particular event or that you expected such probabilities but don't understand why those particular events were chosen?

November 19th, 2009, 04:05 AM  #3 
Newbie Joined: Sep 2009 Posts: 18 Thanks: 0  Re: Markov Chains
I don't get the transition matrix. I would think the matrix would look like this .3333 .6666 .75 .25 For the values...I don't get where those numbers derived from. 
November 19th, 2009, 04:25 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
How did you calculate those values?

November 20th, 2009, 06:59 AM  #5 
Newbie Joined: Sep 2009 Posts: 18 Thanks: 0  Re: Markov Chains
I was thinking 2/3rd's for the first to the marbles and thirty three for the remaining. Likewise for the otherside...I guess stats are kind of my weak link in math.

November 20th, 2009, 07:25 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
That merely tells me that you typed what you thought, but how did you obtain those values? Also, how did you decide in what order to type them in each row?

November 21st, 2009, 06:42 AM  #7 
Newbie Joined: Sep 2009 Posts: 18 Thanks: 0  Re: Markov Chains
From making a Markov Chain like this... 
November 21st, 2009, 07:27 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
Where did the numbers 33, 66, 75, 25 come from, given that "2/3rd's for the first to the marbles" doesn't make sense?

November 23rd, 2009, 09:22 AM  #9 
Newbie Joined: Sep 2009 Posts: 18 Thanks: 0  Re: Markov Chains
Yup, I was being a tard. Usually the case when something isn't making since. Hows 2/5 and 1/5 sound?

November 23rd, 2009, 09:28 AM  #10 
Newbie Joined: Sep 2009 Posts: 18 Thanks: 0  Re: Markov Chains
Yeah, I had all my HW done except for this problem and I was thinking well I'll check and see if anyone replied. I sat down for 2 minutes and was like oh...duh! Figured th rest of the problems out in a couple more minutes...lol. 

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