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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: [mg63033] Re: [mg63004] Re: Using The Random Function to predict Things
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 11 Dec 2005 04:57:16 -0500 (EST)
  • References: <dnbn04$5qv$1@smc.vnet.net> <200512101103.GAA29413@smc.vnet.net> <01BADD95-983F-4969-84BF-00BAD605D411@mimuw.edu.pl>
  • Sender: owner-wri-mathgroup at wolfram.com

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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