x=[-10:10]
>>normpdf(x,0,1)'
ans =
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0001
    0.0044
    0.0540
    0.2420
    0.3989
    0.2420
    0.0540
    0.0044
    0.0001
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000


W= [0.0001
    0.0044
    0.0540
    0.2420
    0.3989
    0.2420
    0.0540
    0.0044
    0.0001]

plot(Y+mu_0,'.');
mu=convn(Y,W,'same');
hold on
plot(mu+mu_0,'-')


normpdf(x,0,9)'

ans =Y
    0.0239
    0.0269
    0.0299
    0.0328
    0.0355
    0.0380
    0.0402
    0.0419
    0.0432
    0.0441
    0.0443
    0.0441
    0.0432
    0.0419
    0.0402
    0.0380
    0.0355
    0.0328
    0.0299
    0.0269
    0.0239

W=[ 0.0328
    0.0355
    0.0380
    0.0402
    0.0419
    0.0432
    0.0441
    0.0443
    0.0441
    0.0432
    0.0419
    0.0402
    0.0380
    0.0355
    0.0328]

>> sum(W)
ans =
    0.5957
W=W/sum(W)
>>sum(W)
ans =
     1

>>normpdf(x,0,1/2)'
ans =
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0003
    0.1080
    0.7979
    0.1080
    0.0003
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000

W=[ 0.0003
    0.1080
    0.7979
    0.1080
    0.0003]

>>sum(W)
ans =
     1.0145
>>W=W/sum(W)
ans =
    0.0003
    0.1065
    0.7865
    0.1065
    0.0003


normpdf(x,0,1/4)'
ans =
         0
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0005
    1.5958
    0.0005
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
         0
W=[0.0005
   1.5958
   0.0005]

>>W=W/sum(W)
W =
    0.0003
    0.9994
    0.0003

>>normpdf(x,0,1/9)'
     ....
    0.0000
    3.5905
    0.0000
    0.0000
     ....
W=1

%Kernel density estimation for unemployment rate data
X=unemployment;
>> min(X)
ans =
    3.9000
>> max(X)
ans =
   10.8000
>> mean(X)
ans =
    6.6913


y=[0:0.1:14];
pdf=zeros(length(y),1/9);
for i=1:length(y)
  pdf(i)= sum(normpdf(y(i)-X,0,1));
end;

pdf=pdf/252
>> sum(0.1*pdf)
ans =
    1.0000
plot(y,pdf,'-');


y=[0:0.1:14];
pdf=zeros(length(y),1);
for i=1:length(y)
  pdf(i)= sum(normpdf(y(i)-X,0,1));
end;

pdf=pdf/252
>> sum(0.1*pdf)
ans =
    1.0000
 
y=[0:0.1:14];
pdf=zeros(length(y),1);
for i=1:length(y)
  pdf(i)= sum(normpdf(y(i)-X,0,4));
end;

pdf=pdf/252
>> sum(0.1*pdf)
ans =
     0.9025