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Math Help - moment generating

  1. #1
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    moment generating

    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!
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  2. #2
    MHF Contributor matheagle's Avatar
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    This has been posted already.
    X is an EXP rv with parameter \beta=3.
    Hence the mean and variance is 3 and 9.

    Finally part (c) is {1\over 3}\int_{6.1}^{6.7} e^{-x/3}dx.
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  3. #3
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    So E(X) is basically the same thing as the mean? Did you just square the parameter / mean to get the variance. For part c, using your equation, I got 0.023727. Thank you for your help.
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by redpack View Post
    So E(X) is basically the same thing as the mean? Did you just square the parameter / mean to get the variance. For part c, using your equation, I got 0.023727. Thank you for your help.
    mu=mean, just ask MOO
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  5. #5
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    Quote Originally Posted by redpack View Post
    Did you just square the parameter / mean to get the variance.
    Thats because the distribution in question is exponential... For a general distribution the general method is to write the moment generating function as a power series and identifying the higher order moments.
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  6. #6
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    Quote Originally Posted by redpack 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!
    First asked here: http://www.mathhelpforum.com/math-he...-function.html

    Thread closed.
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