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Math Help - Expected values & Moment-generating function (MGF)

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    Expected values & Moment-generating function (MGF)

    Having a little trouble with this problem. Thank you in advance!

    A random variable Y has a density function f(y) = e^y, y < 0.
    1. Find E(e^(3Y/2))
    2. Find MFG for Y.
    3. Find V(Y).
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    Re: Expected values & Moment-generating function (MGF)

    Pls don't double post.

    Recall E(x) = \int_{x_1}^{x_2} x f(x)~dx
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    Re: Expected values & Moment-generating function (MGF)

    Quote Originally Posted by charmagne View Post
    Having a little trouble with this problem. Thank you in advance!

    A random variable Y has a density function f(y) = e^y, y < 0.
    1. Find E(e^(3Y/2))
    2. Find MFG for Y.
    3. Find V(Y).
    E(h(Y))=\int_{-\infty}^0 h(y) f(y)\; dy

    so for 1.:

    E(e^{3Y/2})=\int_{-\infty}^0 e^{3y/2}\; e^y\; dy

    which is elementary.

    Now look up the definition of the MGF to do 2., and for 3. you should know that:

    V(Y)=E(Y^2)-\left[ E(Y) \right]^2

    and both of the terms on the right can be obtained from the MGF.

    CB
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