(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that X_{1},....,X_{n}form a random sample from a unifom distribution on the interval [0,1] and that the random variable Y_{n}max{X_{1},....,X_{n}}.

Determine the smallest value of n such that Pr[Y_{n}≥.99]≥.95

2. Relevant equations

W=Y_{n}-Y_{1}where W is the range of the sample

Y_{1}=Z

Y_{n}=W+Z

Y_{1}=min{X_{1},...,X_{n}}

3. The attempt at a solution

f(x)= 1 for 0<x<1

F(x)=x for 0<x<1

h(w,z)=0 unless 0<w<1 and 0<z<1-w

G_{1}(y)=Pr(_{1}<y)= 1-Pr(Y_{1}>y)= 1-[1-F(y)]^{n}

=1-[1-x]

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# Homework Help: Help! Theoretical Stats

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