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# lec1 - Blah Blah Blah A Jogging Problem Joggers enter the...

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Unformatted text preview: Blah Blah Blah A Jogging Problem. Joggers enter the circular jogging loop shown in the figure as a homogeneous Poisson process with rate parameter joggers per hour. Immediately upon entry to the jogging loop each runner flips a fair coin. Outcomes of flips are mutually independent. If the outcome for a particular jogger is Heads , she jogs around the loop in a clockwise manner. If the outcome is Tails , she jogs around the loop in a counter- clockwise manner. The loop is 1/4 mile in length. All joggers run at the same high speed, running at a rate of 8- minute miles. Thus each completes one loop around in 2 minutes. Just before completion of a loop, each jogger again flips a fair coin while running. If the outcome is Heads , she completes her daily run and immediately exits the jogging loop. If the outcome is Tails , she continues without any delay (in the same direction) for at least one more loop. This coin flipping process is continued near the completion of each successful loop until the jogger eventually exits the jogging loop. The Jogging Loop Clockwise Joggers Entering Joggers Exiting Joggers Counter- Clockwise Joggers Find the mean distance jogged by a random...
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lec1 - Blah Blah Blah A Jogging Problem Joggers enter the...

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