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

*To*: mathgroup at smc.vnet.net*Subject*: [mg51745] Re: [mg51725] Re: bimodal distribution in sign of difference of Pi digits]*From*: DrBob <drbob at bigfoot.com>*Date*: Sun, 31 Oct 2004 01:17:15 -0500 (EST)*References*: <200410300748.DAA01148@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Yes, it's a random walk. Bobby On Sat, 30 Oct 2004 03:48:29 -0400 (EDT), Roger Bagula <tftn at earthlink.net> wrote: > > 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/ >> >> > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Re: bimodal distribution in sign of difference of Pi digits]***From:*Roger Bagula <tftn@earthlink.net>