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Geometric density Statistics/Probability

  1. Nov 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose that X_1, X_2, ... are identical and independently distributed with F_x1(x) = exp(x)/(1+exp(x)) for -infinity < x < infinity

    Suppose that N independent of X_i has geometric density f_N (n) = P(N=n) = p(1-p)^(n-1) for n =1,2,3,... and 0<p<1

    Let Z = max{X_1, X_2,.....}.

    What is the cumulative distribution of F_Z(z)?

    For n>0 where n is an integer and z is any real number, what is P(N=n | Z less than or equal to z)


    How would I start this problem?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 3, 2012 #2

    Ray Vickson

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    Re: Statistics/Probability

    I think your statement is incorrect: I would bet that
    [tex] Z = \max \{ X_1, X_2, \ldots, X_N \},[/tex] so on the event {N = n} we have
    [tex] Z = \max \{ X_1, X_2, \ldots, X_n \}.[/tex]
    So, to start, you need do get
    [tex] P \{ Z \leq z | N = n \}[/tex]
    for n = 1,2, ..... . First off, what is this when n = 1?

    RGV
     
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