Re: Tricky Uniform Distribution Problem
I think we had this problem recently and someone pointed out the well known type of distribution for something like this. I forget what it is though.
I like this from-scratch technique. Let F(x) be the probabilty that the max of the numbers is less than x. Then,
F(x) = x^n
ie. the probabilty that all numbers are less than x. But F(x) also represents the Cumulative Distribution Function for the Max random variable. Therefore, its derivative, nx^(n-1), is the pdf for the Max. For the expectation, integrate xnx^(n-1) from 0 to 1 to get n/(n+1).
PairTheBoard
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