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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 (setup 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
 bonnet

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