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Determine the Geometric generating function

  1. Apr 15, 2009 #1
    1. The problem statement, all variables and given/known data

    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 .

    2. Relevant equations



    3. 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?
     
  2. jcsd
  3. Apr 18, 2009 #2
    I have been checking the integral should have been:
    -ln(|1-t|) / t

    and I beleive 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
     
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