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Expected value of the log of a uniform distribution

  1. Aug 24, 2010 #1
    1. The problem statement, all variables and given/known data

    How to calculate the expected value of the log of a uniform distribution?

    2. Relevant equations

    E[X] where X=ln(U(0,1))

    3. The attempt at a solution

    integral from 0 to 1 of a.ln(a) da where a = U(0,1)
    = -1/4

    However I know the answer is -1
     
  2. jcsd
  3. Aug 24, 2010 #2
    Why do you integrate over [tex]a \cdot ln(a)[/tex]?
     
  4. Aug 24, 2010 #3
    Yes, thats not right I see.

    I used this approach instead. To find the first moment of a uniform distribution it is:

    1/(b-a) * integral from a to b of x

    In this case it is

    1/(b-a) * integral from a to b of ln(x)

    Is this ok?

    This approach calculates the correct value for expected value and variance
     
    Last edited: Aug 24, 2010
  5. Aug 24, 2010 #4

    vela

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    Yup, that's the correct method.
     
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