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    Statistics: Moment Generating Function

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    It is attached it is to show that if all Xi are normally distributed then

    Y=a1X1+a2X2+...+anXn

    Also is normally distributed

    But please see the attachment as the question is a bit more specific than that as well. Thanks

    File is uploaded in pdf and word

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    https://brainmass.com/statistics/statistical-theory/statistics-moment-generating-function-581973

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    Solution Preview

    We will use the following properties:
    Lemma 1
    If , then =
    Lemma 2
    If X and Y are independent, then
    ...

    Solution Summary

    Prove, using MGM, that a sum of independent normally distributed variables is also normal.

    $2.19