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uva123
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Homework Statement
Suppose that X1,...,Xn form a random sample from a inform distribution on the interval [0,1] and that the random variable Ynmax{X1,...,Xn}.
Determine the smallest value of n such that Pr[Yn≥.99]≥.95
Homework Equations
W=Yn-Y1 where W is the range of the sample
Y1=Z
Yn=W+Z
Y1=min{X1,...,Xn}
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
G1(y)=Pr(1<y)= 1-Pr(Y1>y)= 1-[1-F(y)]n
=1-[1-x]