Answers to Lab Session 3, Random Variables and Histograms

Task 1:
lab3.task1 <- function(N=10000) 
{
  freq <- seq(0,0,length=6) #generate a vector of 6 zeros
  for (i in 1:N) {
    fourtimes <- sample(1:6,4,replace=T)
    result <- sort(fourtimes)[3] #so "result" is a number between 1 to 6
    freq[result] <- freq[result]+1
  }
  freq <- freq/N
  cat(freq, "\n")
}

Task 2:
y <- c(rep(0,229),rep(1,211),rep(2,93),rep(3,35),rep(4,7),rep(5,1))
observed <- table(y)
lambda <- mean(y)
expected <- c(dpois(0:4,lambda),1-sum(dpois(0:4,lambda)))*length(y)
plot(0:5,observed,type="h",xlab="Number of Deaths",ylab="Frequency")
lines(0:5,expected,col=8)

Task 3:
rhypergeom <- function(N, k, n, m)
{
  # we treat the first k integers as the k red balls; the remaining
  # N-k integers are blue balls
  answer <- seq(0,0,length=m)
  for (i in 1:m) {
    x <- sample(1:N,n,replace=F)
    answer[i] <- sum(x<=k)
  }
  return(answer)
}