In the face of perpetually varying headwinds, cyclists

Chapter 9, Problem 9.41

(choose chapter or problem)

In the face of perpetually varying headwinds, cyclists Lance and Ashwin are in a 3000 mile race across _America. To maintain a speed of v miles/hour in the presence of a 11; mi/ hr headwind, a cyclist must generate a power output y = 50+ (v + VJ - 15)3 Watts. During each mile of road, the 'vind speed W is the continuous uniform (0, 10) random variable independent of the wind speed in any other mile. (a) Lance rides at constant velocity v = 15 mi/ hr mile after mile. Let Y denote Lance's power output over a randomly chosen mile. \tVhat is E[Y]? (b) Ashwin is less powerful but he is able to ride at constant power fJ Watts in the presence of the same variable head'vinds. use the central limit theorem to find iJ such that _Ash,vin 'vins the race 'vith probability 1/ 2.

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