Ten points are evenly spaced around a circle (like a clock face). A particle moves around the circle as follows: Wherever it currently is, it moves counter-clockwise 3 positions with probability 1/3, moves 5 positions clockwise with probability 1/3, and stays where it is with probability 1/3. If the particle starts at the 12 o'clock position, what is the expected number of transitions until it returns to 12 o'clock? 4 3 12 10 24
Ten points are evenly spaced around a circle (like a clock face). A particle moves around the circle as follows: Wherever it currently is, it moves counter-clockwise 3 positions with probability 1/3, moves 5 positions clockwise with probability 1/3, and stays where it is with probability 1/3. If the particle starts at the 12 o'clock position, what is the expected number of transitions until it returns to 12 o'clock? 4 3 12 10 24
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter17: Markov Chains
Section17.6: Absorbing Chains
Problem 7P
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![Ten points are evenly spaced around a circle (like a clock face). A particle moves around the circle as follows: Wherever it currently is, it moves counter-clockwise 3 positions with
probability 1/3, moves 5 positions clockwise with probability 1/3, and stays where it is with probability 1/3. If the particle starts at the 12 o'clock position, what is the expected
number of transitions until it returns to 12 o'clock?
4
3
12
10
24
00000](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5655175-49d2-4db6-a7fd-785d70a02cda%2Fb4df29a9-a849-4fbf-81bb-2de2b040cc2d%2F3ktkzso_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ten points are evenly spaced around a circle (like a clock face). A particle moves around the circle as follows: Wherever it currently is, it moves counter-clockwise 3 positions with
probability 1/3, moves 5 positions clockwise with probability 1/3, and stays where it is with probability 1/3. If the particle starts at the 12 o'clock position, what is the expected
number of transitions until it returns to 12 o'clock?
4
3
12
10
24
00000
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