#===========================================================
# R program to simulate central limit theorem as applied to
# a sum of uniform random variables.
#===========================================================

layout(matrix(c(1,2,3,4),2,2,byrow=TRUE))  # Figure with 4 panels
                                           #  in 2X2 layout.

#-----------------------------------------------------------
# One uniform random variable simulated 10000 times.
#-----------------------------------------------------------
n=1                      # Number of random variables in sum.
repeats=10000            # Number of values to simulate for
                         #  histogram.
v=runif(n*repeats)    # Vector of uniform random variables.
w=matrix(v,n,repeats) # Enter v into a matrix (nXrepeats).
y=colSums(w)             # Sum the columns.
hist(y,freq=FALSE,breaks=20,ann=FALSE)  # Histogram.
title("n = 1")

#-----------------------------------------------------------
# Sum of two uniform random variables simulated 10000 times.
#-----------------------------------------------------------
n=2                      # Number of random variables in sum.
repeats=10000            # Number of values to simulate for
                         #  histogram.
v=runif(n*repeats)       # Vector of uniform random variables.
w=matrix(v,n,repeats)    # Enter v into a matrix (nXrepeats).
y=colSums(w)             # Sum the columns.
hist(y,freq=FALSE,breaks=20,ann=FALSE)  # Histogram.
title("n = 2")

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

n=5                      # Number of random variables in sum.
repeats=10000            # Number of values to simulate for
                         #  histogram.
v=runif(n*repeats)       # Vector of uniform random variables.
w=matrix(v,n,repeats)    # Enter v into a matrix (nXrepeats).
y=colSums(w)             # Sum the columns.
hist(y,freq=FALSE,breaks=20,ann=FALSE)  # Histogram.
title("n = 5")

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