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Distribution of the digits of Pi

If we plot the digits of $\pi$

$3.1415926535897932384626433832795028841971693993751058\cdots$

versus the indices

$((1, 3), (2, 1), (3, 4), (4, 1), \cdots)$

How to quantify the randomness of the resultant curve?

The first part of the curve looks like this .

Re: @Henning Makholm

Rephrasing the question, suppose the curve happens to be a sample function of a random process, how to give the distribution of that random process?

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    In one quite important sense they are _not random at all_, because they are the one and only sequence that are _the decimal digits of $\pi$_. That's an extremely specific property.2012-12-15
  • 2
    You might like to take a look at [Normal Numbers](http://en.wikipedia.org/wiki/Normal_number).2012-12-15
  • 1
    There are lots of ways to try to quantify randomness. Which are appropriate will depend on what you intend to do with the result.2012-12-15

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