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 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
