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Df to pdf

  1. Mar 2, 2009 #1
    I have been asked to determine the pdf given a DF.

    F(x) = 0 for x<0
    F(x) = x^2/x for x 0<= x < 1
    F(X) = x/2 for 1<=x<2
    F(x) = 1 for x>= 2

    Is the pdf the derivative of the df

    So if you wanted the probability of x between 0 and 1
    The pdf would just be x ?


    regards
    Brendan
     
  2. jcsd
  3. Mar 2, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Surely this isn't right? did you mean x^2/2, so that F is continuous at x=1?

    You don't need the pdf at all to answer that question. F(x) is the probability that the random variable is between 0 and x. The probablity that x is between 0 and 1 is just F(1)= 1/2.

    The pdf is the function
    f(x)= 0 for x< 0
    f(x)= x for [itex]0\le x< 1[/itex]
    f(x)= 1/2 for [itex]1\le x< 2[/itex]
    f(x)= 0 for [itex]2\le x[/itex]
     
  4. Mar 2, 2009 #3
    Thanks alot. You are right it is x^2/2 my mistake.
    So does that mean if x = 1/2 , F(1/2) = 1/2 ?
     
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