# R code for Exercise 3.3.

############################################################
#
# x is an array of numbers
# areDifferent returns 1 if all elements of x are unique
# areDifferent returns 0 if some element of x is duplicated
#
############################################################

areDifferent = function(x) {
  if(length(unique(x)) == length(x))
    return(1)
  else
    return(0)
}

############################################################
#
# nsample is the number of samples, by default, 10,000.
# n is the sample size, by default, 5
# x is an nsample by n matrix where each row can be thought
#   of as a random sample of n digits from 0 to 9
#
############################################################

sampleDigits = function(nsample=10000,n=5) {
  x = matrix(sample(0:9,size=nsample*n,replace=T),nrow=nsample,ncol=n)
  return(x)
}

############################################################
#
# x is a matrix where each row is a sample of random digits
# results is the return value, an array of length nrow(x)
#   which is 1 if the entire row is different
#   and 0 if there is a duplicate on the corresponding row
#
############################################################

getResults = function(x) {
  results = apply(x,1,areDifferent)
  return(results)
}

############################################################
#
# x is an array of 0s and 1s indicating the outcome
#   of each trial (0 is failure, 1 is success)
# p is the theoretical probability
#
# plotResults makes a plot similar to those on page 82
#   to show how the relative frequency changes as the
#   number of samples increases.
#
# cumsum computes the cumulative sum, so the ith element of cumsum(x)
#   equals the total number of successes in the first i trials
# cumsum(x) / 1:n is the relative frequency of success for each i from 1 to n
#
# invisible() instructs R to not priont anything when the function is complete.
#
############################################################

plotResults = function(x,p) {
  n = length(x)
  plot(1:n,cumsum(x)/1:n,type="l",ylim=c(0,1),xlab="Sample number",ylab="Relative Frequency")
  abline(h=p,lty=2,col=2)
  invisible()
}