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Omni-MATH / Dan is walking down the left side of a street in New York City and must cross to…

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problem

Dan is walking down the left side of a street in New York City and must cross to the right side at one of 10 crosswalks he will pass. Each time he arrives at a crosswalk, however, he must wait tt seconds, where tt is selected uniformly at random from the real interval [0,60](t[0,60](t can be different at different crosswalks). Because the wait time is conveniently displayed on the signal across the street, Dan employs the following strategy: if the wait time when he arrives at the crosswalk is no more than kk seconds, he crosses. Otherwise, he immediately moves on to the next crosswalk. If he arrives at the last crosswalk and has not crossed yet, then he crosses regardless of the wait time. Find the value of kk which minimizes his expected wait time.
Plain-text mathematical notation (without MathML)
Dan is walking down the left side of a street in New York City and must cross to the right side at one of 10 crosswalks he will pass. Each time he arrives at a crosswalk, however, he must wait t seconds, where t is selected uniformly at random from the real interval [0,60](t can be different at different crosswalks). Because the wait time is conveniently displayed on the signal across the street, Dan employs the following strategy: if the wait time when he arrives at the crosswalk is no more than k seconds, he crosses. Otherwise, he immediately moves on to the next crosswalk. If he arrives at the last crosswalk and has not crossed yet, then he crosses regardless of the wait time. Find the value of k which minimizes his expected wait time.
Original LaTeX notation
Dan is walking down the left side of a street in New York City and must cross to the right side at one of 10 crosswalks he will pass. Each time he arrives at a crosswalk, however, he must wait $t$ seconds, where $t$ is selected uniformly at random from the real interval $[0,60](t$ can be different at different crosswalks). Because the wait time is conveniently displayed on the signal across the street, Dan employs the following strategy: if the wait time when he arrives at the crosswalk is no more than $k$ seconds, he crosses. Otherwise, he immediately moves on to the next crosswalk. If he arrives at the last crosswalk and has not crossed yet, then he crosses regardless of the wait time. Find the value of $k$ which minimizes his expected wait time.

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Source and history

task_id
e2f12498-3c68-593e-a8c6-c0f08f31fe73
task_key
test--e2f12498-3c68-593e-a8c6-c0f08f31fe73
task_revision_id
1
config / split
/ test

Official source

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