# CLT
nSample=10;nRep=10^5;
x=matrix(runif(nSample*nRep),nrow=nSample);
x.means<-colMeans(x)
hist(x.means,50,main='Distribution of Means of Uniform Distribution', 
 xlab='Means', probability=T)
x.means.dens<-density(x.means)
lines(x.means.dens,lwd=3,lty=1,col='red')
x2=seq(0,1,0.001);CLT=dnorm(x2,mean=0.5,sd=(sqrt(1/12))/(sqrt(nSample)))
lines(x2,CLT,lwd=3,lty=3,col='cyan')
legend("topright",c("Density of Actual Means","Normal Distribution"), 
 lty=c(1,3), col=c('red','cyan'),lwd=3)

# LAW of LARGE NUMBER
dat<-sample(1:6,1000,replace=T)
prob6<-cumsum(dat==6)/(1:1000)
par(mfrow=c(2,1))
plot(dat,type='p',col="red",main="results of 1000 rolls of a die",xlab="rolls",
 ylab="outcome", pch=20)
plot(prob6,type='l',main="Cumulative probability that rolls of a die come out SIX",
 xlab="rolls", ylab="probability",lwd=3,ylim=c(0.0,0.5))
abline(h=1/6,col='red',lwd=2,lty=2)


# WHILE
r=-99;v1=1633;v2=355
while (r!=0){
  r=v1%%v2
  print(paste('v1 =',v1,', v2 = ',v2,',remainder = ',r))
  v1=v2
  v2=r
}

# REPEAT
v1=1633;v2=355;
repeat {
  r=v1%%v2
  print(paste("v1 =",v1,",v2 = ",v2,",remainder = ",r))
  v1=v2;v2=r
  if (r==0){ break}
 }