For the random variable:

P(Y=0)= 1/8, P(Y=1)=1/2, P(Y=3)=3/8

Find the MGF of Y, and E[Y] and Var(Y).

Helpppp, I reallly don't have a clue how to do this!

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- Dec 9th 2009, 02:36 AM #1

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- Dec 9th 2009, 03:19 AM #2

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If X is a finite random variable taking on values x1, x2, . . ., xn, the

**mean**or**expected value**of X, written μ, or E(X), is

μ = E(X) = x1.P(X = x1) + x2.P(X = x2) + . . . + xn.P(X = xn) = ∑ (xi.P(X = xi))If X is a random variable, its**variance**is defined to be

σ2 = E( [X - μ]2 ). Its**standard deviation**is defined to be the square root σ of the variance.

replace X by Y ...

- Dec 9th 2009, 03:31 AM #3
Start by applying the defintions!

By definition of MGF: $\displaystyle m(t) = E(e^{tY}) = \frac{1}{8} + \frac{1}{2} e^t + \frac{3}{8} e^{3t}$.

By definition: $\displaystyle E(Y) = \left. \frac{dm}{dt}\right|_{t = 0} = ....$

By definition: $\displaystyle Var(Y) = E(Y^2) - [E(Y)]^2$. And by definition $\displaystyle E(Y^2) = \left.\frac{d^2m}{dt^2}\right|_{t = 0} = ....$

- Dec 9th 2009, 06:14 AM #4

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- Dec 9th 2009, 04:14 PM #5
You're expected to know the theorem given here regarding the moment generating function of a sum of independent random variables: Moment-generating function - Wikipedia, the free encyclopedia

**Edit:**Asked here: http://www.mathhelpforum.com/math-he...ution-mgf.html. Thread closed.