/*** a ***/
%let limit1=0;
%let limit2=1;
%let seed=573392;


data integral1;
call streaminit(&seed);

 do i=1 to 10000;
  x=&limit1+rand("UNIFORM")*(&limit2-&limit1);
  y1=exp(x)/(1+exp(x**2));
  y2=&limit2-&limit1;
  y=y1/y2;
  sum+y;
  int1=sum/i;
  diff2+(y-int1)**2;
  var=diff2/(i-1);
  stde=sqrt(var/i);
  output;
 end;
 run;



 /*** b ***/
%let abeta=5;
%let bbeta=1;


data integral3;
call streaminit(&seed);

 do i=1 to 10000;
  x=rand("BETA",&abeta,&bbeta) ;
  y1=exp(x)/(1+exp(x**2));
  y2=PDF("BETA",x,&abeta,&bbeta);
  y=y1/y2;
  sum+y;
  int1=sum/i;
  diff2+(y-int1)**2;
  var=diff2/(i-1);
  stde=sqrt(var/i);
  output;
 end;
 run;

  /*** c ***/
%let abeta=2;
%let bbeta=2;


data integral4;
call streaminit(&seed);

 do i=1 to 10000;
  x=rand("BETA",&abeta,&bbeta) ;
  y1=exp(x)/(1+exp(x**2));
  y2=PDF("BETA",x,&abeta,&bbeta);
  y=y1/y2;
  sum+y;
  int1=sum/i;
  diff2+(y-int1)**2;
  var=diff2/(i-1);
  stde=sqrt(var/i);
  output;
 end;
 run;


 /*** d ***/
 %let h=0.5;


data integral5;
call streaminit(&seed);

 do i=1 to 10000;
  x=rand("TRIANGLE",&h) ;
  y1=exp(x)/(1+exp(x**2));
  y2=(x <= &h)*2*x/&h + (x>&h) * 2*(1-x)/(1-&h);  **(...) je logièki izraz sa rezultatom 0 ili 1;
  y=y1/y2;
  sum+y;
  int1=sum/i;
  diff2+(y-int1)**2;
  var=diff2/(i-1);
  stde=sqrt(var/i);
  output;
 end;
 run;

 /*** e ***/
 %let h=0.77;


data integral6;
call streaminit(&seed);

 do i=1 to 10000;
  x=rand("TRIANGLE",&h) ;
  y1=exp(x)/(1+exp(x**2));
  y2=(x <= &h)*2*x/&h + (x>&h) * 2*(1-x)/(1-&h);  **(...) je logièki izraz sa rezultatom 0 ili 1;
  y=y1/y2;
  sum+y;
  int1=sum/i;
  diff2+(y-int1)**2;
  var=diff2/(i-1);
  stde=sqrt(var/i);
  output;
 end;
 run;


   /*** f ***/

%let m=0.77;
%let s=0.385;

/** Truncated normal na intervalu (0,1) ***/

 data _NULL_;
  probn1=probnorm((&limit1-&m)/&s);
  probn2=probnorm((&limit2-&m)/&s);
  probn=probn2-probn1;
  call symput("probn",probn);
  put probn1 probn2 probn;
  run;



data integral2;
call streaminit(&seed);

 do while (i<10000);

  x=rand("NORMAL",&m,&s) ;
  if x>= &limit1 and x <= &limit2 then do;
  i+1;
  y1=exp(x)/(1+exp(x**2));
  y2=pdf('NORMAL',x,&m,&s)/&probn;
  y=y1/y2;
  sum+y;
  int1=sum/i;
  diff2+(y-int1)**2;
  var=diff2/(i-1);
  stde=sqrt(var/i);
  output;
  end;
 end;
 run;