Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 05 (a)
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Question B 05 (a) 

Suppose four towns are connected by roads in the configuration shown below. A random driver wakes up every morning and flips a coin. If the coin is heads, she stays where she is for the day. If the coin is tails, she drives to the next town, choosing one of the roads with no preference. (For example, if she leaves Town A, she is equally likely to go to Town B or Town C, but she will not go to Town D that day.) (a) Write the probability transition matrix for the random driver. Use the ordering A, B, C, D. 
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Hint 

Let be the probability of moving to state if you are in state . Then the transition matrix matrix is defined by . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Coin head and coin tail are equally distributed with possibility . If the driver starts at B for example, the possibility that he stays at B is equal to coin head, which is . If he gets coin tail, he can move to A, C, or D. The possibility for each one is . Based on this, we get the probability transition matrix Answer: 