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Proof: Quantile Function Property

  1. Nov 13, 2011 #1
    1. The problem statement, all variables and given/known data
    F-1 is the quantile function of a general random variable X and has the following property that is analogous to the property of the c.d.f.
    Prove: Let x0 = limp→0,p>0 F-1(p) and x1 = limp→1,p<1 F-1(p). Then x0 equals the greatest lower bound on the set of numbers c such that Pr(X≤c) > 0, and x1 equals the least upper bound on the set of numbers d such that Pr(X≥d) > 0.

    3. The attempt at a solution
    I'm not too sure where to begin with proving this problem...
    My interpretation of the problem is that x0 and x1 are the (lowest?) lower and (greatest?) upper bounds such that Pr(X=x) > 0.
     
  2. jcsd
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