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QA

What is Benford's law?

For numbers in natural form, the probability of the first digit being 1 is about 30%, and the probability of 2 being 17.6%, decreasing in order. The probability of the first digit being 8 and 9 is only 5.1% and 4.6% respectively.

\(d\in\{1, ..., 9\}\)

\[P(d) = \log _{10}(d+1)- \log _{10}(d) = \log _{10}(\frac{d+1}{d}) =\log _{10}(1+ \frac{1}{d}) \]


It also has a limitation, that is, the number is at least more than 3000.

1    30.1%    
 
2    17.6%    
 
3    12.5%    
 
4    9.7%    
 
5    7.9%    
 
6    6.7%    
 
7    5.8%    
 
8    5.1%    
 
9    4.6%    

You may be curious, shouldn't this be average? Why is the probability of 1 appearing very high?

Sorry, no one knows why.

This may be a law of this world.

 

This article was last edited at 2020-11-12 17:14:28

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