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Possible Duplicate:
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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    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

1 Answers 1

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Histogram of the first 10000 digits

Digits of Pi

Covariance of the first 10000 consecutive digits: -0.09 (negligible)


Mathematica code used:

Histogram:

Histogram[RealDigits[Pi, 10, 10000][[1]], 10] 

Covariance: (I'm sure there's a more efficient way to do this)

N[Covariance[RealDigits[Pi, 10, 10000][[1]][[Range[1, 9999]]],     RealDigits[Pi, 10, 10000][[1]][[Range[2, 10000]]]]] 
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    If any of you guys have more requests, I'll be happy to compute/plot more data.2012-12-15