Part B. I don\'t understand how to do it so please explain too. 4. (15pts) There

Question

Part B. I don't understand how to do it so please explain too.

4. (15pts) There are n runners in a 100m dash race. Each runner runs a time that is uniformly distributed between 9.5 and 10.5 seconds. For simplicity let us normalize this to having the time be uniformly distributed between [0,1] (i.e. a standard uniform distribution). Each runner runs a time independent of the other runners. The world record at the 100m dash is approximately 9.6 seconds (which would be 0.1 on the standard uniform distribution) a. (5pts) What is the probability that if n - 2, the (normalized) winning time (i.e. the minimum time) breaks the world record (has a time

Explanation / Answer

If n = 2 then

The equation would be Pr(Y<0.2) = 1 - (1 - 0.2)2= 1 - 0.82= 1 - 0.64 = 0.36.

So the expected value of willing time (normalized) is 0.36.

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