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Unformatted text preview: Pstat160 Winter 2010 Extra examples of limiting probabilities You should be very comfortable doing the first 2 problems. Make sure you do them on your own first , and only after reading the handout and your notes! Then look at the solution IN DETAIL! Think of the reasons behind each steps , not just trying to remember ‘that’s just what you have to do’ Third problem is more challenging and should be for more advanced students. Problem pb 24 (set-up was done in discussion 6) Define the state to be the color of the ball just selected, and let 1=red, 2=white, 3=blue. To find the transition probability say P 11 , we need to find the probability to select a red ball from urn red, which is 1 4+1 = 1 / 5. We can find all transitions the same way and get P = 1 / 5 4 / 5 2 / 7 3 / 7 2 / 7 3 / 9 4 / 9 2 / 9 We need to find the limiting probabilities π . The set of linear equations are π (1) = 1 / 5 π (1) + 2 / 7 π (2) + 3 / 9 π (3) π (2) = 3 / 7 π (2) + 4 / 9 π...
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This note was uploaded on 01/10/2011 for the course STAT 160A taught by Professor Bonnet during the Winter '10 term at UCSB.
- Winter '10