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Homework Help: Finding expected value from moment generating function

  1. Feb 17, 2010 #1
    Find E(X) given the moment generating function

    M_X (t) = 1 / (1-t^2)

    for |t| < 1.

    (The pdf is f(x) = 0.5*exp(-|x|), for all x, so graphically you can see that E(X) should be 0.)


    I know that E(X) = M ' _X (t) = 0

    BUT M ' _X (t) = 2x / (1-x^2)^2 which is indeterminate at 0 so maybe you need L'Hopital's rule or something but I can't get it to work. How do you do this?
  2. jcsd
  3. Feb 17, 2010 #2
    What makes you say it's indeterminate at 0?
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