#===========================================================
# Figure 14.4.R.
# Simulation of central limit theorem.
#===========================================================

layout(matrix(c(1,2,3,4),2,2,byrow=TRUE))

#-----------------------------------------------------------
# One uniform random variable simulated 10000 times.
#-----------------------------------------------------------
size=1                   # Number of random variables in sum.
repeats=10000            # Number of values to simulate for
                         #  histogram.
v=runif(size*repeats)    # Vector of uniform random variables.
w=matrix(v,size,repeats) # Enter v into a matrix (sizeXrepeats).
y=colSums(w)             # Sum the columns.
hist(y,freq=FALSE,ann=FALSE)       # Histogram.
title("size 1")

#-----------------------------------------------------------
# Sum of two uniform random variables simulated 10000 times.
#-----------------------------------------------------------
size=2                   # Number of random variables in sum.
repeats=10000            # Number of values to simulate for
                         #  histogram.
v=runif(size*repeats)    # Vector of uniform random variables.
w=matrix(v,size,repeats) # Enter v into a matrix (sizeXrepeats).
y=colSums(w)             # Sum the columns.
hist(y,freq=FALSE,ann=FALSE)       # Histogram.
title("size 2")

#-----------------------------------------------------------
# Sum of five uniform random variables simulated 10000 times.
#-----------------------------------------------------------

size=5                   # Number of random variables in sum.
repeats=10000            # Number of values to simulate for
                         #  histogram.
v=runif(size*repeats)    # Vector of uniform random variables.
w=matrix(v,size,repeats) # Enter v into a matrix (sizeXrepeats).
y=colSums(w)             # Sum the columns.
hist(y,freq=FALSE,ann=FALSE)       # Histogram.
title("size 5")

#-----------------------------------------------------------
# Sum of twenty uniform random variables simulated 10000 times.
#-----------------------------------------------------------
size=20                  # Number of random variables in sum.
repeats=10000            # Number of values to simulate for
                         #  histogram.
v=runif(size*repeats)    # Vector of uniform random variables.
w=matrix(v,size,repeats) # Enter v into a matrix (sizeXrepeats).
y=colSums(w)             # Sum the columns.
hist(y,freq=FALSE,ann=FALSE)       # Histogram.
title("size 20")