- #1

- 292

- 1

First of all, can anyone explain to me in English what exactly the Moment Generating Function is? The book does a poor job at it and the teacher wasn't very clear either. In fact, the book *never* says what it is at all, just how it's used.

## Homework Statement

If you toss a fair die with outcome X, p(x) = 1/6 for x=1,2,3,4,5,6. Find M

_{x}(t).

## Homework Equations

[tex]M_x(t) = E(e^{tx}) = \sum_{x\in D}e^{tx}p(x) [/tex]

## The Attempt at a Solution

If we start with the Expectation equation above:

[tex]\sum_{x\in D}e^{tx}p(x) = \sum_{x=1}^6 e^{tx}(1/6)[/tex]

[tex]= e^{t\cdot 0}(1/6) + e^{t\cdot 1}(1/6) + e^{t\cdot 2}(1/6) + ... e^{t\cdot 6}(1/6)[/tex]

[tex] = 1 + \frac{e^t}{6} + \frac{e^{2t}}{6} + \frac{e^{3t}}{6} + \frac{e^{4t}}{6} + \frac{e^{5t}}{6} + \frac{e^{6t}}{6}[/tex]

First of all, is this correct so far? And if it is, since it's been umteen years since I've had algebra, what happens here? How can this be simplified?