Re: bimodal distribution in sign of difference of Pi digits]

*To*: mathgroup at smc.vnet.net*Subject*: [mg51725] Re: bimodal distribution in sign of difference of Pi digits]*From*: Roger Bagula <tftn at earthlink.net>*Date*: Sat, 30 Oct 2004 03:48:29 -0400 (EDT)*Reply-to*: tftn at earthlink.net*Sender*: owner-wri-mathgroup at wolfram.com

Dear jasonp, I don't know. This method is a new way to investigate Pi digits. I had done some counts of base ten digits frequencies before this. I have no real explaination of why the difference is higher in higher number of digits. The groups of positive "Sign"s should random. It is Sign[x]-> {-1,0,1} depending on the difference in consecutive differences. It is the probability of a digit pair: {a,b}--> Sign[a-b] p=Probability [a]*Probability[b] If they are equal as p0: p->p0^2 If the Mathematica for such a probability would be: p0->Random[Integer,{0,9}] as a Distribution Since this is an straight type probabilty and not a Gaussian the probabilies are equal and should be over a long term 1/10 each or a total of p-->1/100 different for different combinations: {a>b}->+1,{a-1},{a=b}->0 at {4/10,4/10,2/10} that gives something like 4/1000,4/1000,2/1000 I'm not seeing that kind of behavior except for the bimodal which is expected as (a=b) is only about 2/10 of the 1/100 and I'm seeing more zeros than that. It appears to be a much more complex distribution. I want to try E and orther irrational numbers by this method as well! I'm glad you asked as I hadn't thought to do a probability analysis until now! I can simulate the probability above in Mathematica and see what I get and compare them. jasonp at boo.net wrote: >Quoting Roger Bagula : > > > >>(* Sum of the sign of the differences between the first 2000 digits of Pi*) >> >> > >Shouldn't this behave like a random walk, i.e. the variance >increases over time? > >jasonp > > >------------------------------------------------------ >This message was sent using BOO.net's Webmail. >http://www.boo.net/ > > > -- Respectfully, Roger L. Bagula tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : alternative email: rlbtftn at netscape.net URL : http://home.earthlink.net/~tftn

**Follow-Ups**:**Re: Re: bimodal distribution in sign of difference of Pi digits]***From:*DrBob <drbob@bigfoot.com>