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Math Help - Derive the moment-generating function of Y bar

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    Derive the moment-generating function of Y bar

    Suppose that Y1, Y2, , Yn are independent, normally distributed random variables with mean u and
    variance \sigma^2 . Define
    Y bar= \displaystyle \sum^n_{i=1} Yi/n


    Derive the moment-generating function of Y bar
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  2. #2
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    Re: Derive the moment-generating function of Y bar

    Quote Originally Posted by wopashui View Post
    Suppose that Y1, Y2, , Yn are independent, normally distributed random variables with mean u and
    variance \sigma^2 . Define
    Y bar= \displaystyle \sum^n_{i=1} Yi/n


    Derive the moment-generating function of Y bar
    What have you tried? Where are you stuck?
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    Re: Derive the moment-generating function of Y bar

    Quote Originally Posted by mr fantastic View Post
    What have you tried? Where are you stuck?
    srooy, i don't know how to start the question, do i start by definition m(t)= E(e^tybar)= integral e^tybar times f(y) then sub in the summation into the integral, but what is f(y)here, do we use the normal density function?
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    Re: Derive the moment-generating function of Y bar

    Quote Originally Posted by wopashui View Post
    srooy, i don't know how to start the question, do i start by definition m(t)= E(e^tybar)= integral e^tybar times f(y) then sub in the summation into the integral, but what is f(y)here, do we use the normal density function?
    Given!!:

    Yn are independent, normally distributed random variables with mean u and
    variance img.top {vertical-align:15%;} .
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  5. #5
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    Re: Derive the moment-generating function of Y bar

    well linear combo's of normals is a normal, hence just compute moo and sigma squared of y bar.
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    Re: Derive the moment-generating function of Y bar

    Quote Originally Posted by matheagle View Post
    well linear combo's of normals is a normal, hence just compute moo and sigma squared of y bar.
    then how do you find the mgf with moo and the variance, we know that m'(0)=moo, and m''(0)-[m'(0)]^2= variance
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