# [R] Need some help

azzza azza.khogaliali at utoronto.ca
Tue Oct 16 20:53:08 CEST 2007

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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.

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