# [R] Need some help

azzza azza.khogaliali at utoronto.ca
Tue Oct 16 21:49:27 CEST 2007

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THANKYOU guyz! yes, Jim's code was right (it was similar to someone
Yes, that was exactly what i was looking for. lastly, how do i find the

Marc Schwartz wrote:
>
> On Tue, 2007-10-16 at 11:53 -0700, azzza wrote:
>>
>>
>> ok, so suppose a coin is tossed 1000 times. Each time head occurs, we win
>> a
>> dollar, otherwise we lose a dollar. Let S(n) be our accumulated winnings
>> after n tosses. For instance, if the sequence HHHTT occurs in the first
>> five
>> tosses, then S(5) = \$1.00 wheras if the sequence HTTTT occurs, S(5) =-\$3.
>> So
>> now, we want to see how many times during the 1000tosses S9n) will go
>> from a
>> positive balance to a negative balanc eor the other way around. So for
>> our
>> simulation, S(n) is computed by adding one to S(n-1) if a head occurs,
>> and
>> subtracting one form S(n-1) if a tail occurs. A change in sign will occur
>> on
>> the nth toss in one of two ways: S(n-2)=1, S(n-1)=0 and, S(n)= -1 OR
>> S(n-2)
>> = -1, S(n-1)=0 and S(n)=1. This is equivalent to S(n-2)+ S(n-1)+ S(n)=0.
>> so now, n is the numbe rof tosses,  S(n) is the number of heads minus the
>> number of tails in n tosses and C is the number of times S(n) changes
>> sign.
>> so we initialize n=0, S(-1)=0, S(0)=0, and C(0)=0
>>
>> now we should,
>> -generate u, a uniform number, with the increment, n=n+1 ....(our n=1000)
>> -if u<1/2, that is tails occur, set S(n)=S(n-1)-1, and also set
>> S(n)=S(n-1)+1
>> - If S(n) +S(n-1)+S(n-2)=0, then increment C=C+1.
>>
>> My issue is simulating this in R, where I need to code the number of sign
>> changes, the frequency of heads, and to plot S(n) versus n in a line
>> graph.
>>
>>
>> for each coin toss, the number of sign changes could either be a positive
>> number, zero, or a negative number.
>
> I believe that Jim had the right approach in his reply here:
>
>   https://stat.ethz.ch/pipermail/r-help/2007-October/143383.html
>
> and Prof. Koenker has given you a reference on the theory:
>
>   https://stat.ethz.ch/pipermail/r-help/2007-October/143385.html
>
> HTH,
>
> Marc
>
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