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

**References**:**Re: Using The Random Function to predict Things***From:*Peter Pein <petsie@dordos.net>