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## Homework Statement

Let f(x) = 2x 0<x<1

a) Determing the Moment Generating function M(t) of X

b) Use the MGT to determine all moments about the origin

c) Give the 3rd central moment called the skewness

## Homework Equations

## The Attempt at a Solution

a) [tex]\int^1_0 e^{tx}2x dx = \frac{2xe^{tx}}{t} - \int^1_0 e^{tx}2 dx

= \frac{2}{t}(xe^{tx} - e^t + 1)[/tex]

b)

[tex]E\left(X^n\right)=M^{(n)}(0)=\left.\frac{\mathrm {d}^n M_(t)}{\mathrm{d}t^n}\right|_{t=0}[/tex]

[tex]E\left(X^n\right)=M^{(n)}(0)=\left.\frac{\mathrm {d}^n \frac{2}{t}(xe^{tx} - e^t + 1)}{\mathrm{d}t^n}\right|_{t=0}[/tex]

Is that what I'm supposed to do for part b)?

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