% Exercise 1.24: MATLAB has a built-in Gaussian random number generator
%   randn with mean mu = 0 and standard deviation sigma = 1.  Test this
%   random variable by constructing an incidence histogram; i.e., divide
%   [-4,4] into say 80 subintervals (bins), call randn 1000 times, and
%   count the number of times the variable falls into each bin.  Normalize
%   by the number of calls and graph against (1.15).
%
% Answer (developed for MATLAB 6.1) :
%
N = 1000;                     % number of trials
a = -4;                       % left-hand side of the interval
b = 4;                        % right-hand side of the interval
nb = 80;                      % number of bins
d = (b-a)/nb;                 % size of one bin
bins = zeros(1,nb);           % initialize the bins
for i=1:N                     % perform N trials
  r = randn;                  % generate random number
  if r >= a & r <= b          % only treat number in [a,b]
     k = floor((r-a)/d)+1;    % index of the bin
     bins(k) = bins(k) + 1;   % update the bins
  end;
end;
plot(bins*(b-a)/N);           % normalized plot
hold on                       % we make graph of (1.15) 
s = a:0.1:b;                  % range for sampling 
f = exp(-s.^2/2)/sqrt(2*pi);  % sample the function
plot(f)                       % graphs normal distribution