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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
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