% DSAMPLE file dsample.m  Simulates sample from discrete population
% Version of 12/31/95 (Display revised 3/24/97)
% Relative frequencies vs probabilities for
% sample from discrete population distribution
X  = input('Enter row matrix of VALUES  ');
PX = input('Enter row matrix of PROBABILITIES  ');
n  = input('Sample size n  ');
U  = rand(1,n);
T  = dquant(X,PX,U);
[x,fr] = csort(T,ones(1,length(T)));
disp('    Value      Prob    Rel freq')
disp([x; PX; fr/n]')
ex = sum(T)/n;
EX = dot(X,PX);
vx = sum(T.^2)/n - ex^2;
VX = dot(X.^2,PX) - EX^2;
disp(['Sample average ex = ',num2str(ex),])
disp(['Population mean E[X] = ',num2str(EX),])
disp(['Sample variance vx = ',num2str(vx),])
disp(['Population variance Var[X] = ',num2str(VX),])