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Math Help - moment generating function

  1. #1
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    moment generating function

    If the moment generating function of X is M(t)=\frac{1}{1-3t}, t<\frac{1}{3}

    A. Find E(X)
    B. Find Var(X)
    C. P(6.1 < x < 6.7)

    Thank you in advance for your help!
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by logitech View Post
    If the moment generating function of X is M(t)=\frac{1}{1-3t}, t<\frac{1}{3}

    A. Find E(X)
    B. Find Var(X)
    C. P(6.1 < x < 6.7)

    Thank you in advance for your help!
    By definition, E(X^n)=M^{(n)}(0), where M^{(n)} denotes the n-th derivative of the mgf.

    Specifically, E(X)=M'(0) and E(X^2)=M''(0)

    For Var(X), recall the formula I put before : E(X)-[E(X)]


    For question C., I don't know... Your mgf is the mgf of an exponential distribution with parameter 1/3, which would finish the question, by using the cumulative distribution function.

    I'm looking for a way without "recognizing" the mgf, but it looks like there isn't any.
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  3. #3
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    This one is still difficult for me to understand. Thank you for trying to help me understand this one. I will keep working on it. I wish you could be my tutor! Taking an online class basically means there is no teacher, just a textbook and a list of work to do.
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  4. #4
    MHF Contributor matheagle's Avatar
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    MGF's are unique
    This is a gamma with \alpha=1 and \beta=3

    Hence the mean is \alpha\beta=3
    and the variance is \alpha\beta^2=9
    and yes, ms mathbeagle, now you can integrate the density to obtain the probabilities.
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  5. #5
    Flow Master
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    Quote Originally Posted by logitech View Post
    If the moment generating function of X is M(t)=\frac{1}{1-3t}, t<\frac{1}{3}

    A. Find E(X)
    B. Find Var(X)
    C. P(6.1 < x < 6.7)

    Thank you in advance for your help!
    See this thread also: http://www.mathhelpforum.com/math-he...enerating.html
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