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Is an expected value of fx(x) the same as this expected value?

  1. Sep 9, 2013 #1
    If a probability density function is fx(x) = 5x^4 for 0<x<1 and 0 elsewhere, then the expected value of E[x^0.5] is the integral of ∫x^0.5*fx(x) between 0 and 1 which is 10/11.

    However if I try to approach it as the expected value of Y=X^0.5 then I find fy(y) = 5*lny/y^4 and its expected value is 20/33.

    What's wrong? Is it a right approach or are those two things different?
     
  2. jcsd
  3. Sep 9, 2013 #2
    Ah, I got it, x is y^2.. not the other way around.
     
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