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Cdf of continous RV transformation

  1. Sep 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f(x)= 2x , 0<x<1 , zero elsewhere, be the pdf of X.
    Compute the cdf of Y=1/X
    2. Relevant equations

    cdf of X = p(X< x)




    3. The attempt at a solution

    P(1/X <= y)
    = P(X <= 1/y)
    int 2x from 0 to 1/y
    = x^2 eval from 0 to 1/y
    = 1/y^2

    so the cdf is 1/y^2 for 1<y<infinty

    however i don't think this is right.... the text book answers state the cdf as 1-1/y^2


    so im confused. thanks for any help!
     
  2. jcsd
  3. Sep 24, 2011 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Since 2 < 4, does this imply that 1/2 < 1/4?

    RGV
     
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