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Sum of discrete uniform random variables

  1. Sep 12, 2014 #1
    1. The problem statement, all variables and given/known data
    Let ##X_k## be iid uniform discrete on ##\{0,...,9\}##. Find the distribution of ##\sum\limits_{k=1}^{\infty} \frac{X_k}{10^k}##


    2. Relevant equations



    3. The attempt at a solution
    I've tried a lot of things, I've tried decomposing ##X_k## into 10 bernoulli trials, I've tried using some form of central limit theorem. I've tried calculating the characteristic functions, then taking the limit and I get something really ugly. Any hints? I feel like there is some limit theorem I don't know.
     
  2. jcsd
  3. Sep 12, 2014 #2

    Ray Vickson

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    If you observe ##Y = \sum_{k=1}^{\infty} X_k / 10^k## you will see a random number between 0 and 1 and whose decimal digits are iid uniformly distributed in 0--9. How do you think such a number will be distributed?
     
    Last edited: Sep 12, 2014
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