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## Author: Joshua M. Tebbs
## Date: 30 June 2018
## Update: 10 November 2018
## STAT 511 course notes: R Code
## Chapter 2
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# Figure 2.1
# Page 2
n = 10000 # number of simulations
flip = rbinom(n,1,0.5)
# Create plot of the relative frequencies
# Initialise
rel.freq = flip*0
for (i in 1:n){
	rel.freq[i] = sum(flip[1:i])/i
	}
plot(rel.freq,ylab="Relative frequency",xlab="Number of flips",type="o",pch=20,cex.lab=1.25)
abline(h=0.5,lty=2)
sum(flip)


# Figure 2.2
# Page 4
n = 10000 # number of simulations
M = 10 # number of men
event = seq(1,n,1)*0
hats = matrix(0,n,M)
for (i in 1:n){
	hats[i,]<-sample(seq(1,M,1),replace=FALSE)
	match = hats[,1]*0
	for (j in 1:M){
	if (hats[i,j]==j) match[j]<-1 else match[j]<-0
		}
	if (sum(match)>0) event[i]<-1 else event[i]<-0
	}	
sum(event)
# Create plot of the relative frequencies
# Initialise
rel.freq = event*0
for (i in 1:n){
	rel.freq[i] = sum(event[1:i])/i
	}
plot(rel.freq,ylab="Relative frequency",xlab="Number of trials",type="o",pch=20,cex.lab=1.25)


# Figure 2.3
# Page 5
n = 10000 # number of simulations
M = 50 # number of students
event = seq(1,n,1)*0
birthday = matrix(0,n,M)
for (i in 1:n){
	birthday[i,]<-sample(seq(1,365,1),size=M,replace=TRUE)
	if (length(unique(birthday[i,]))<M) event[i]<-1 else event[i]<-0
	}
sum(event)
# Create plot of the relative frequencies
# Initialise
rel.freq = event*0
for (i in 1:n){
	rel.freq[i] = sum(event[1:i])/i
	}
plot(rel.freq,ylab="Relative frequency",xlab="Number of trials",type="o",pch=20,cex.lab=1.25)