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% make up an m-file, gaussian.m containing
%   function y=gaussian(x,m,s); % m=mean, s=stddev
%   % note 1/sqrt(2*pi) = .3989422803
%   y=(.3989422803/s)*exp(-0.5*((x-m)./s).^2);
x=[-10:.1:10]; y=gaussian(x,0,1);
plot(x,y); hold on;
y=gaussian(x,0,2); plot(x,y);
y=gaussian(x,0,4); plot(x,y);

              Exercises/Experiments
1.
particles=500; steps=40;
for k=1:particles
   steplog=fix(2*rand(1,steps)); % ran. vec. of 0's/1's
   steplog = 2*steplog-1; % ran. vec. of -1/+1
   place(k) = sum(steplog); % endpt for this 40 step walk
end
x=-20:2:20;
hist(place,x)

1a.
% Eqn (6.2.9) is the gaussian with mean=0 and
% stddev = sqrt(2Dt).  Therefore make an m-file
% gaussian.m, (already done in Section 2.6, repeated here)
%    function y=gaussian(x,m,s);
%    y=(.3989422803/s)*exp(-0.5*((x-m)./s).^2);
% Part (a)
D=1; t=1; s=sqrt(2*D*t);
x=[-10:.1:10]; y=gaussian(x,0,s);
plot(x,y); hold on;
D=1; t=2; s=sqrt(2*D*t);
y=gaussian(x,0,s); plot(x,y);
D=1; t=3; s=sqrt(2*D*t);
y=gaussian(x,0,s); plot(x,y);