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 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.

 Tags chains, markov

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# urn a contains 2 red and 3 blue marbles, and urn b contains 4 red and 1 blue marble

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