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Finding expectation of peicewise mixed distribution density function

  1. Mar 22, 2012 #1
    If I am given the CDF of a piecewise mixed distribution density starting from a and ending at b, would the expected value just be a + integral(all the pieces) ?
     
  2. jcsd
  3. Mar 22, 2012 #2

    HallsofIvy

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    If there were only one "piece" would the expected value be a+ the integral of that piece?
     
  4. Mar 22, 2012 #3
    I suppose not. It would just be the integral of that piece. But if it were two or more?
     
  5. Mar 23, 2012 #4

    chiro

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    Hey torquerotates.

    Why don't you just differentiate each piece of your CDF and then use the definition of expectation?

    If you function is in discrete form or a form that is non-integrable (non-Riemannian) then you can either just look at the deltas if you have a discrete distribution for that piece, or if its in a Lebesgue form just use the properties of the characteristic function to get your PDf for that piece.
     
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