表の出る確率0.8のコインを投げ続けるとどうなるか。
N = 1000 # Specify the total number of flips, denoted N.
pHeads = 0.8 # Specify underlying probability of heads.
# Flip a coin N times and compute the running proportion of heads at each flip.
# Generate a random sample of N flips (heads=1, tails=0):
flipSequence = sample( x=c(0,1), prob=c(1-pHeads,pHeads), size=N, replace=TRUE )
# Compute the running proportion of heads:
r = cumsum( flipSequence ) # Cumulative sum: Number of heads at each step.
n = 1:N # Number of flips at each step.
runProp = r / n # Component by component division.
# Graph the running proportion:
plot( n , runProp , type="o" , log="x" , col="skyblue" ,
xlim=c(1,N) , ylim=c(0.0,1.0) , cex.axis=1.5 ,
xlab="Flip Number" , ylab="Proportion Heads" , cex.lab=1.5 ,
main="Running Proportion of Heads" , cex.main=1.5 )
# Plot a dotted horizontal reference line:
abline( h=pHeads , lty="dotted" )
# Display the beginning of the flip sequence:
flipLetters = paste( c("T","H")[flipSequence[1:10]+1] , collapse="" )
displayString = paste0( "Flip Sequence = " , flipLetters , "..." )
text( N , .9 , displayString , adj=c(1,0.5) , cex=1.3 )
# Display the relative frequency at the end of the sequence.
text( N , .8 , paste("End Proportion =",runProp[N]) , adj=c(1,0.5) , cex=1.3 )
