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Homework Help: Change of variable

  1. Sep 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Let X be a random variable with pdf f(x)=2x , for 0<x<1 and let Y=X^2, find the cdf of Y.

    2. Relevant equations



    3. The attempt at a solution

    cdf = P(Y<=y) = P(X^2<=y)

    [tex]= P(-\sqrt{y}\leq X\leq \sqrt{y})[/tex]

    [tex]=\int^{\sqrt{y}}_{-\sqrt{y}}2x dx [/tex]

    = 0 for 0<y<1

    Am i correct?
     
    Last edited: Sep 6, 2010
  2. jcsd
  3. Sep 6, 2010 #2

    vela

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    You're close. Remember that f(x) is non-zero only on the interval [0,1].
     
  4. Sep 6, 2010 #3
    Thanks Vela, but why did i get 0 for the interval [0,1]
     
  5. Sep 6, 2010 #4

    vela

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    Again: f(x) is non-zero only on the interval [0,1].
     
  6. Sep 6, 2010 #5
    What is the significance of that?
     
  7. Sep 6, 2010 #6

    vela

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    Check your limits of integration, keeping in mind my previous posts.
     
  8. Sep 6, 2010 #7
    do i adjust the limit of the integration?
     
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