/* Here we do summation and integration */


proc iml;

n=200;
sum=0;
do i=1 to n;
a=1/i**2;
sum=sum+a;
print i a sum;
end;

sum=0; iter=0;
do until(a<0.0001);
iter=iter+1;
a=1/iter**2;
sum=sum+a;
print iter a sum;
end;

sum=0;
d=0.5;
n=101;
do i=1 to n by d;
a1=1/i**2;
a2=1/(i+d)**2;
sum=sum+d*(a2+a1)/(2);
end;
print sum;

a=1/1-1/101;
print a;


start f(z);
m=5;
s=1;
f=z*(1/(s*sqrt(2*3.14159265)))*exp(-((z-m)**2)/(2*(s**2)));
return(f);
finish f;




del=0.01;
sum=0;
do i=-50 to 50 by del;
pdf1=f(i);
pdf2=f(i+del);
h=(pdf1+pdf2)/2;
area=del*h;
sum=sum+area;
*print area sum;
end;

print sum;



start f(z);
f=(1/sqrt(2*3.14159265))*exp(-(z**2)/2);
return(f);
finish f;



del=0.01;
sum=0;
do i=-5 to 1.645 by del;
pdf1=f(i);
pdf2=f(i+del);
h=(pdf1+pdf2)/2;
area=del*h;
sum=sum+area;
*print area sum;
end;

print sum;




start f(z);
f=(1/sqrt(2*3.14159265))*exp(-(z**2)/2);
return(f);
finish f;

del=0.1;
sum=0;
do i=-5 to 5 by del;
pdf1=f(i);
pdf2=f(i+del);
h=min(pdf1,pdf2);
rarea=del*h;
tarea=abs(pdf1-pdf2)*del/2;
sum=sum+rarea+tarea;
*print area sum;
end;

print sum;