# Simulates 100 coin tosses, finds longest run of heads, repeats 10000 times, examines distribution of longest runs
#
# modify this program for different/general values of n (number of tosses), N (number of repetitions)
#
x=c("H","T")
#
# initialize vector of longruns
longruns = rep(NA, times = 10000)
#
# begin loop across number of repetitions
for (j in 1:10000) {
#
# initialize longrun and current run
longrun = 0
run=0
#
# generate 100 random coin tosses
y=sample(x,100,replace=TRUE)
#
# now start the loop that goes through the coin tosses to calculate runs of heads
for (i in 1:100) {
#
# if current toss is H, increment run by one
if (y[i] == "H") {run = run + 1} else {run = 0}
#
# if current run exceeds longrun, replace longrun with current run
if (run > longrun) longrun = run
}
#
# after all 100 coin tosses are analyzed, record longest run for this repetition 
longruns[j] = longrun
}
results=table(longruns); results
mean(longruns)
hist(longruns)
long5 = (longruns > 5)
table(long5)
prob = sum(long5/10000); prob