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. ______________________________________________ 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. -- View this message in context: http://www.nabble.com/Need-some-help-tf4624513.html#a13240042 Sent from the R help mailing list archive at Nabble.com. ______________________________________________ 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.
