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November 25th, 2011, 09:04 PM   #1
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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 . Define



Derive the moment-generating function of Y bar
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November 26th, 2011, 02:04 PM   #2
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Re: Derive the moment-generating function of Y bar

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Originally Posted by 450081592
Suppose that Y1, Y2, , Yn are independent, normally distributed random variables with mean u and
variance . Define



Derive the moment-generating function of Y bar
I prefer working with characteristic functions. The characteristic function for Yk is exp(i?t-{(?t)^2}/2). Therefore for Yk/n it is exp(i?t/n-{(?t/n)^2}/2). For Y bar it is exp(i?t-{(?t)^2}/(2n)).

You can get the moments by expanding the characteristic function in powers of t, or by recognizing that Ybar is normally distributed with mean ? and variance (?^2)/n.
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