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Thread: Use the moment-generating function to find the mean

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    Use the moment-generating function to find the mean




    I have the moment-generating function for the discrete uniform distribution f(x)=\frac{1}{k} for x=1,2,...k:

    Mx(t)=\frac{e^t(1-e^t)}{k(1-e^t)}

    I need to take the derivative of this function with respect to t then find the limit as t approaches 0. I've tried L'Hospital's Rule for this limit with no luck. Any suggestions?

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    Re: Use the moment-generating function to find the mean

    Are you sure you have the correct mgf? To me it looks very close but there is a slight difference from what I would expect.
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    Re: Use the moment-generating function to find the mean

    I made a mistake. It should be Mx(t)=\frac{e^t(1-e^{kt})}{k(1-e^t)}. Although, I think I run into the same problem.
    Last edited by Buckeye; 07-23-2016 at 09:37 PM.

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    Re: Use the moment-generating function to find the mean


    Mx'(t)=\frac{(k-ke^t)(e^t-e^{kt+t}(k+1))+ke^t(e^t-e^{kt+t})}{(k-ke^t)^2}

    \lim_{t\to 0}Mx'(t)= \mu However, this is of the form 0/0. If I use L'Hospital's rule, I will continue to get 0/0. Any suggestions?

    What is the use of this mgf if it isn't helpful?

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