% 
% Written by:
% -- 
% John L. Weatherwax                2006-12-31
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; 
close all; clear; 

qj = [ 5     6   1   1   2   2   2   2 ]; 
pj = [ 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 ];
N  = length(qj);

% Note: see the codes "max_adj_return*.m" for perhaps a better way to do use MATLAB's unbounded optimization routine
wj = fminsearch( @(x) min_std_dev_fn(x,pj,qj), (1/N)*ones(1,N-1) ); 
% "create" the probabilty we must assign to the last horse:
wj = [ wj(:); 1-sum(wj) ]; wj = wj(:)'; 

wj

% compute the mean and standard deviation: 
%
m = sum( pj .* wj .* ( qj + 1 ) ) - 1 

uncer = sqrt( sum( pj .* ( wj .* ( qj + 1 ) - 1 - m ).^2 ) )