A Using Statistics to Test for Normality of Pi

WWGD
Science Advisor
Homework Helper
Messages
7,678
Reaction score
12,342
Is there a " reasonable" way to test for the normality of ##\pi## , i .e., that every digit occurs with the same frequency? Someone suggested randomly sampling strings of size 20 and outputting the frequency. Then I guess we could average the frequencies among samples , use a chi-squared test. Assuming random sampling can be done, is this a sound way of testing?
 
Last edited by a moderator:
Physics news on Phys.org
Yes. The Chi-squared goodness of fit test can be used to test if the digits are from a uniform distribution.
 
Is normality dependent upon the base - is it possible for there to be a pattern in one base that then appears random in another?

anyway, here is one method that showed normality out to 22.5 trillion base 10 decimal places and an equivalent number of hexideximal ones

https://arxiv.org/pdf/1612.00489.pdf
 
Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
Thread 'Detail of Diagonalization Lemma'
The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in the second step in the last line, where we have an m-overlined, and we substitute the expression for m. Are we saying that the name of a coded term is the same as the coded term? Thanks in advance.

Similar threads

Replies
7
Views
2K
Replies
30
Views
2K
Replies
27
Views
3K
Replies
20
Views
3K
Replies
20
Views
4K
Replies
1
Views
3K
Back
Top