# mean no. of cars per household

population=c(rep(0,5),rep(1,3),rep(2,2));
max.cars=max(population);

sample.sizes=c(1,2,4,16);
n.sizes=length(sample.sizes);

no.of.samples = 10000; 

n=c(); ybar = c();
for (i in 1:n.sizes) {
  sample.size = sample.sizes[i];
  if (sample.size > 1)  samples = t( replicate(no.of.samples,sample(population,sample.size,replace=T)) )
  if (sample.size == 1) samples = matrix(sample(population, no.of.samples,replace=T),nrow=no.of.samples,ncol=1) 
  possible.means.of.n = apply(samples,1,mean);
  n=c(n,rep(paste("n = ",toString(sample.size)),no.of.samples));
  ybar = c(ybar,possible.means.of.n)
 }
    
pdf(file = "ave-number-cars.pdf",
    width = 4, height = 6, family = "Helvetica")
    
   histogram(
   ~ ybar | n ,
   breaks = seq(-1/32,2+1/32,1/16), 
   main =  "", 
   xlab=  "mean no. of cars in sample of size n" 
 )
 
dev.off()
 

# mean no. of letters per word

require(lattice)

ds=read.table("NewsweekWords_1_column.txt",as.is=T,col.names="word")
attach(ds)
word.length=nchar(word)
summary(word.length)
max.length=max(word.length)

sample.sizes=c(1,2,4,16);
n.sizes=length(sample.sizes);

n=2; no.of.samples = 10000; 

n=c(); ybar = c();
for (i in 1:n.sizes) {
  sample.size = sample.sizes[i];
  if (sample.size > 1)  samples = t( replicate(no.of.samples,sample(word.length,sample.size,replace=T)) )
  if (sample.size == 1) samples = matrix(sample(word.length, no.of.samples,replace=T),nrow=no.of.samples,ncol=1) 
  possible.means.of.n = apply(samples,1,mean);
  n=c(n,rep(paste("n = ",toString(sample.size)),no.of.samples));
  ybar = c(ybar,possible.means.of.n)
 }

pdf(file = "ave-number-letters.pdf",
    width = 4, height = 6, family = "Helvetica")
    
   histogram(
   ~ ybar | n ,
   breaks = seq(1-1/32,15+1/32,1/16), 
   main =  "", 
   xlab=  "mean no. letters/word in sample of size n" 
 )
 
dev.off()