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Homework Help: Help! Theoretical Stats

  1. May 10, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose that X1,....,Xn form a random sample from a unifom 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

    2. Relevant equations

    W=Yn-Y1 where W is the range of the sample
    Y1=Z
    Yn=W+Z
    Y1=min{X1,...,Xn}


    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
    G1(y)=Pr(1<y)= 1-Pr(Y1>y)= 1-[1-F(y)]n
    =1-[1-x]
     
  2. jcsd
  3. May 11, 2010 #2

    statdad

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    Homework Helper

    Why are you considering the range? Your question concerns the maximum of the sample.

    Two hints, using your notation of [itex] Y_n [/itex] as the maximum value.
    a) If [itex] Y_n \le y [/itex], you know that [itex] X_i \le y [/itex] for [itex] i = 1, 2, \dots, n[/itex]

    b) The individual [itex] X_i [/itex] values are independent

    This should allow you to get the CDF of [itex] Y_n [/itex]
     
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