function [o,v,b,V1]=optimal2(U,subset)
% generates optimal linear combination of five estimators and outputs 
% average estimator and variance. 
% subset is set of possible indices e.g. [1 2 4 5]
% how does this differ from optimal???
Y1=(.53/2)*(fn(.47+.53*U)+fn(1-.53*U));
Y2=.37*.5*(fn(.47+.37*U)+fn(.84-.37*U))+.16*.5*(fn(.84+.16*U)+fn(1-.16*U));
Y3=.37*fn(.47+.37*U)+.16*fn(1-.16*U);
intg=2*(.53)^3+.53^2/2;
Y4=intg+fn(U)-GG(U);
Y5=importance('fn',U);
X=[Y1' Y2' Y3' Y4' Y5'];
X=X(:,subset);
mean(X)
V=cov(X);
Z=ones(length(subset),1);
V1=inv(V);
b=V1*Z/(Z'*V1*Z);
o=mean(X*b);
v=1/(Z'*V1*Z);   % the variance per uniform input.... so divide by n

