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MathGroup Archive 2005

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Re: Re: Using The Random Function to predict Things

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63034] Re: [mg63004] Re: Using The Random Function to predict Things
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 11 Dec 2005 04:57:24 -0500 (EST)
  • References: <dnbn04$5qv$1@smc.vnet.net> <200512101103.GAA29413@smc.vnet.net> <01BADD95-983F-4969-84BF-00BAD605D411@mimuw.edu.pl> <A89D6ED2-C1B1-4EAA-9DFB-8D263F6A4DD6@mimuw.edu.pl>
  • Sender: owner-wri-mathgroup at wolfram.com

I have to make more corrections. Firstly, I meant, of course ,   
"until successive k heads come up". And secondly, one should start  
nesting with a "digital coin throw" Random[Integer] rather than with  
0, so the correct code is:

simulate[k_]:=NestWhileList[Random[Integer]&,Random[Integer],Plus[##] 
=!=k&,k]

Andrzej


On 11 Dec 2005, at 10:54, Andrzej Kozlowski wrote:

> On 11 Dec 2005, at 10:46, Andrzej Kozlowski wrote:
>
>
>> A simple way to simulate tossing a coin until three heads come up is:
>>
>>
>> simulate[k_]:=NestWhileList[Random[Integer]&,0,Plus[##]=!=k&,k]
>
>
> I meant "until k heads come up".
>
>
> Andrzej Kozlowski
>
>
>
>>
>>
>> On 10 Dec 2005, at 20:03, Peter Pein wrote:
>>
>>> mathuser schrieb:
>>>> Hi there friends...
>>>> I used this line of code "typicalList = Table[Random[Integer],  
>>>> {50}]" and got this result...
>>>>
>>>> {1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1,  
>>>> 0, 0, 0, 0, \
>>>> 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0,  
>>>> 1, 1, 0, 1}
>>>>
>>>> By generating a few more of these random lists, I'm to predict a  
>>>> similiar situation: such as how long i would expect to wait for  
>>>> 3 heads in a coin tossing competition...
>>>>
>>>> any suggestion or help as to what code i could use to do this?
>>>>
>>>> thanks a lot guys
>>>>
>>> Hi,
>>>
>>> in this kind of sequence you've got 2^k possibilities of k  
>>> subsequent
>>> numbers. One of them consits of k times the one. As 1 and 0 occur  
>>> with
>>> the same probability, one would expect to wait on average 2(2^k-1)
>>> "tosses" of digits.
>>>
>>
>> This answer is, of course, correct. In fact the answer to the  
>> question "how many flips of a coin are needed on the average  to  
>> get any specified pattern" is well known and due to A. D. Solvev.  
>> The whole problem is solved in detail in Knuth's book "Concrete  
>> Mathematics" ( see particularly page 394 in the chapter "Discrete  
>> Probability").
>>
>> A simple way to simulate tossing a coin until three heads come up is:
>>
>>
>> simulate[k_]:=NestWhileList[Random[Integer]&,0,Plus[##]=!=k&,k]
>>
>> For example:
>> simulate[5]
>>
>>
>> {0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0, 
>> 0,0,0,1,\
>> 1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,1 
>> ,0,0,1,0,\
>> 0,1,1,0,1,1,0,0,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0 
>> ,1,0,0,0,\
>> 1,1,1,0,0,1,1,1,1,0,1,1,0,0,1,1,1,1,1}
>>
>>
>> Andrzej Kozlowski
>


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