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A statistical study of randomness among the first 5,00,000 digits of Pi (π)

Author Affiliations

  • 1Maharashtra University of Health Sciences, Nashik, MS, India

Res. J. Mathematical & Statistical Sci., Volume 6, Issue (3), Pages 1-5, March,12 (2018)

Abstract

A large amount of work has been done on the randomness of the digits of Pi (π) with various statistical tests of randomness which are used to distinguish good from not-so-good random number generators when applie d to the digits of Pi (π). Sampling and simulation are the vital are as in statistics. In both of these areas random sample i s the basic requirement to arrive at correct decision. To draw random sample, lots of methods ranging from lottery method to computer based random number generation are readily available. The digits of Pi (π) have to pass the tests as well as from the good random number generator (RNG) can be easily and rapid ly generate in the computer. I have made an interesting study in the statement in which first 5,00,000 digits of Pi (π) were divided into various consecutive blocks and each block was tested for randomness by using Chi-square test goodness of fit. A statistical analysis of the first 5,00,000 digits of Pi (π) was carried out with a view to examine, in close detail, the degree of randomness in the frequency and in the order of appear ance of the various digits therein. Frequency counts were done fo r single digits within blocks of 5000; 10,000 and 20 ,000 of digits of Pi (π). Calculation of the various statistical quan tities shows that the sets of digits under analysis confirm closely to the hypothesis of perfect randomness.

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