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## 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?