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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- Nov 30th 2011, 08:47 PMcharmagneExpected 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). - Nov 30th 2011, 09:19 PMpickslidesRe: Expected values & Moment-generating function (MGF)
Pls don't double post.

Recall $\displaystyle E(x) = \int_{x_1}^{x_2} x f(x)~dx$ - Dec 1st 2011, 12:16 AMCaptainBlackRe: Expected values & Moment-generating function (MGF)
$\displaystyle E(h(Y))=\int_{-\infty}^0 h(y) f(y)\; dy$

so for 1.:

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

which is elementary.

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

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

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

CB