centralLimitTheorem.R

# Eric Gullufsen
# Visualize the central limit theorem

# take 10, 50, 100, 1000 random samples of size ten of integers in [0, 10]
# take average of each one
# plot these

# the resulting probability density function will look incresingly 'normal'
# as n increases - the number of samples taken

SAMPLE_SPACE <- 0:10
SAMP_SIZE <- 10

ns <- c(10, 50, 100, 1000, 2000)

for (n in ns)
{
  counts <- vector(mode="numeric", length = n)
  
  # regions of the possible values the mean can take on
  regs <- seq(0, 10, length.out = (n + 1))
  
  # make vector of midpoints of the region for plotting
  regs_mid <- c()
  for (c in 1:n)
  {
    regs_mid <- c(regs_mid, ((regs[c] + regs[(c + 1)]) / 2))
  }
  
  # simulate the runs, using runif and floor to generate the random integers
  for (i in 1:n)
  {
    # generate randoms
    samp <- floor(runif(10, 0, 11))
    meme <- mean(samp)
    # counting the number of runs giving a mean value within each of the regions
    for (j in 1:n)
    {
      if ((meme >= regs[j]) && (meme < regs[(j + 1)]))
        counts[j] <- counts[j] + 1
    }
  }
  
  probs <- counts / n
  
  plot(regs_mid, probs, type="h", xlab="Expected Value", ylab="Probability")
  legend(x="topleft", legend=c(paste("n = ", toString(n))), bty="n")
  
  # plot(regs_mid, probs, type="p")
  # legend(x="topleft", legend=c(paste("n = ", toString(n))), bty="n")
}