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Homework Help: Moment generating function

  1. Nov 13, 2012 #1
    given m(t) = (1-p+p*e^t)^5
    what is probability P(x<1.23)

    i know that m(t) = e^tx * f(x)
    m'(0) = E(X)
    and m''(0) , can find the var(x)
    should i calculate it using a normal table?
  2. jcsd
  3. Nov 13, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    No, m(t) is not e^tx * f(x), but it is ∫{e^(tx) f(x) dx: x=0..∞}.

    Why would you use a normal table when the random variable is very far from normal? You can actually work out explicitly what is the distribution by expanding out the power and collecting terms in e^(kt) for k = 0,1,2,3,4,5.

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