Determine the Geometric generating function

[boneill3]

Homework Statement

Suppose RX(t) = E[(1 − tX)−1] is called the geometric generating function
of X. Suppose the random variable Y has a uniform distribution on (0, 1); ie
fY (y) = 1 for 0 < y < 1. Determine the geometric generating function of Y .

Homework Equations

The Attempt at a Solution

E[(1-tY)^-1] = \int (1-ty)^-1 f_Y(y) dy

-ln(|yt-1|) / t

Do I than take the Taylor series of the result to give the geometric generating function for Y?

 

[boneill3]

I have been checking the integral should have been:
-ln(|1-t|) / t

and I believe that this is the generation function of Y.

To find the value E[X^3] of -ln(|1-t|) / t
apparently I have to take the taylor series of -ln(|1-t|) / t
and read off the 3rd moment.

I'm a bit lost Any Help greatly appreciated

regards
Brendan