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Math Help - MGF moment help?

  1. #1
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    MGF moment help?

    If X has the moment generating function
    M(t) = (e^ ((PI)*t ) - e^ (et) ) / t
    find E (X), V ar (X), and P (2.8 <= X < 3). help please?
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  2. #2
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    What you need to do get E[X] is to evaluate the first derivative of M(t) at t=0.

    E[X]=\frac{d}{dt}M(0)

    For the variance, you need to find the second derivative of M(t) and E[X].

    Var(X)=E[X^2]-(E[X])^2=\frac{d^2}{dt^2}M(0)-(E[X])^2

    I hope that helps.
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  3. #3
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    I don't think that function works or is correct. I think my professor made a mistake because the limit as t approaches 0 of M(t) is π - e, but this limit should always be 1.
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  4. #4
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    Use the derivatives, and it will work.
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  5. #5
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    I know this will sound like the dumbest question ever, but I'm never sure when to apply derivatives or integrals!
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  6. #6
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    i got what i got before
    1.24
    http://www.wolframalpha.com/input/?i=(-e^2+%2B+pi^2)/2
    the limit of the derivative of the mgf
    as t approaches 0 is that function
    and that function is not 1
    oh wait, but thats allegedly the mean
    i dunno, i don't think its a pdf
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  7. #7
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    Quote Originally Posted by Intsecxtanx View Post
    I don't think that function works or is correct. I think my professor made a mistake because the limit as t approaches 0 of M(t) is π - e, but this limit should always be 1.
    You're correct. The given function is not a valid mgf, for the very reason you state.

    Quote Originally Posted by akolman View Post
    Use the derivatives, and it will work.
    Since the given function is not a valid mgf there is no point doing this.
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