clc
close
clear
format long
syms x a
p1=int(exp(2*x),-0.5,0);
p2=int(exp(-2*x),0,0.5)

double(p1+p2)

total=1000000;
c=0;
for i=1:total
    rnd=rand();
    if(rnd<=0.5)
        rnd1=0.5*rand();
         v=0.5 *log(2*rnd1); 
    else
         rnd2=0.5*rand();
         v=-0.5 *log(1-2*rnd2); 
    end

         if( v>=-0.5 && v<=0.5)
           c=c+1; 
         end
end
(c/total)

clc
close
clear
format long
syms t a  b  y c x1 x2 u1 u2 uy E_YX1  E_YX2 E_X1X2 E_X12 E_X22 x


total=100000;
c=0;
for i=1:total
  rnd=rand();
  if(rnd<=1/4)
     v= sqrt(rand()*(1/4) * 4)+2;
  else
     u=rand()*(3/4);
     v=-sqrt(-12*u +9)+6;
  
  end
  if( v>2.5 && v<3.5)
     c=c+1; 
  end
end
c/total

p1=int(0.5*(x-2),2.5,3);
p2=int(0.5*(2-(x/3)),3,3.5);
double(p1+p2)