diff --git a/Lectures_my/EMPP/2016/Lecture4/Exercises/Error_propagation/result.png b/Lectures_my/EMPP/2016/Lecture4/Exercises/Error_propagation/result.png
index 86e4ebe..60424fa 100644
--- a/Lectures_my/EMPP/2016/Lecture4/Exercises/Error_propagation/result.png
+++ b/Lectures_my/EMPP/2016/Lecture4/Exercises/Error_propagation/result.png
Binary files differ
diff --git a/Lectures_my/EMPP/2016/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C b/Lectures_my/EMPP/2016/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C
index 138b29d..d6f9611 100755
--- a/Lectures_my/EMPP/2016/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C
+++ b/Lectures_my/EMPP/2016/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C
@@ -1,167 +1,73 @@
-Double_t sqr(Double_t x){return x*x;}
+// This program can be execute from the command line as folows:
+//
+//      root -l foam_kanwa.C
+//_____________________________________________________________________________
+
+#include "Riostream.h"
+#include "TFoam.h"
+#include "TCanvas.h"
+#include "TH2.h"
+#include "TMath.h"
+#include "TFoamIntegrand.h"
+#include "TRandom3.h"
+
+//_____________________________________________________________________________
+Double_t sqr(Double_t x){return x*x;};
+//_____________________________________________________________________________
 Double_t Camel2(Int_t nDim, Double_t *Xarg){
-  // 2-dimensional distribution for FOAM, normalized to one (within 1e-5)
+// 2-dimensional distribution for Foam, normalized to one (within 1e-5)
   Double_t x=Xarg[0];
   Double_t y=Xarg[1];
   Double_t GamSq= sqr(0.100e0);
-  Double_t Dist=exp(-(sqr(x-1./3) +sqr(y-1./3))/GamSq)/GamSq/TMath::Pi();
-  Dist        +=exp(-(sqr(x-2./3) +sqr(y-2./3))/GamSq)/GamSq/TMath::Pi();
+  Double_t Dist= 0;
+  Dist +=exp(-(sqr(x-1./3) +sqr(y-1./3))/GamSq)/GamSq/TMath::Pi();
+  Dist +=exp(-(sqr(x-2./3) +sqr(y-2./3))/GamSq)/GamSq/TMath::Pi();
   return 0.5*Dist;
 }// Camel2
-Int_t kanwa(){
-  // TH2D  *hst_xy = new TH2D("hst_xy" ,  "x-y plot", 50,0,1.0, 50,0,1.0);
+//_____________________________________________________________________________
+
+Int_t foam_kanwa(){
+  cout<<"--- kanwa started ---"<<endl;
+  TH2D  *hst_xy = new TH2D("hst_xy" ,  "x-y plot", 50,0,1.0, 50,0,1.0);
   Double_t *MCvect =new Double_t[2]; // 2-dim vector generated in the MC run
-  TRandom3  *PseRan   = new TRandom3();  // Create random number generator
-  PseRan->SetSeed(4357);                // Set seed
+  //
+  TRandom     *PseRan   = new TRandom3();  // Create random number generator
+  PseRan->SetSeed(4357);
   TFoam   *FoamX    = new TFoam("FoamX");   // Create Simulator
-  FoamX->SetkDim(2);          // No. of dimensions, obligatory!
-  FoamX->SetnCells(500);      // No. of cells, can be omitted, default=2000
-  FoamX->SetRhoInt(Camel2);   // Set 2-dim distribution, included below
-  FoamX->SetPseRan(PseRan);   // Set random number generator
-  FoamX->Initialize();        // Initialize simulator, takes a few seconds...
-  // From now on FoamX is ready to generate events according to Camel2(x,y)
-  for(Long_t loop=0; loop<100000; loop++){
-    FoamX->MakeEvent();          // generate MC event
-    FoamX->GetMCvect( MCvect);   // get generated vector (x,y)
+  FoamX->SetkDim(2);         // No. of dimensions, obligatory!
+  FoamX->SetnCells(500);     // Optionally No. of cells, default=2000
+  FoamX->SetRhoInt(Camel2);  // Set 2-dim distribution, included below
+  FoamX->SetPseRan(PseRan);  // Set random number generator
+  FoamX->Initialize();       // Initialize simulator, may take time...
+  //
+  // visualising generated distribution
+  TCanvas *cKanwa = new TCanvas("cKanwa","Canvas for plotting",600,600);
+  cKanwa->cd();
+  // From now on FoamX is ready to generate events
+  int nshow=5000;
+  for(long loop=0; loop<100000; loop++){
+    FoamX->MakeEvent();            // generate MC event
+    FoamX->GetMCvect( MCvect);     // get generated vector (x,y)
     Double_t x=MCvect[0];
     Double_t y=MCvect[1];
     if(loop<10) cout<<"(x,y) =  ( "<< x <<", "<< y <<" )"<<endl;
-    //hst_xy->Fill(x,y);           // fill scattergram
+    hst_xy->Fill(x,y);
+    // live plot
+    if(loop == nshow){
+      nshow += 5000;
+      hst_xy->Draw("lego2");
+      cKanwa->Update();
+    }
   }// loop
-  Double_t mcResult, mcError;
-  FoamX->GetIntegMC( mcResult, mcError);  // get MC integral, should be one
-  cout << " mcResult= " << mcResult << " +- " << mcError <<endl;
-  // now hst_xy will be plotted visualizing generated distribution
-  // TCanvas *cKanwa = new TCanvas("cKanwa","Canvas for plotting",600,600);
-  //cKanwa->cd();
-  //   hst_xy->Draw("lego2");
-  return 1;
+  //
+  hst_xy->Draw("lego2");  // final plot
+  cKanwa->Update();
+  //
+  Double_t MCresult, MCerror;
+  FoamX->GetIntegMC( MCresult, MCerror);  // get MC integral, should be one
+  cout << " MCresult= " << MCresult << " +- " << MCerror <<endl;
+  cout<<"--- kanwa ended ---"<<endl;
+
+  return 0;
 }//kanwa
 
-
-double phi(int n, double *Xarg)
-{
-  double x=Xarg[0];
-  return exp(-x*x/2.)/sqrt(TMath::Pi()*2);
-}
-void PhimFoam()
-{
-  TRandom3  *PseRan   = new TRandom3();  // Create random number generator
-  TFoam   *FoamX    = new TFoam("FoamX");   // Create Simulator
-  FoamX->SetkDim(1);          // No. of dimensions, obligatory!
-  FoamX->SetRhoInt(phi);   // Set 1-dim distribution, included below
-  FoamX->SetPseRan(PseRan);   // Set random number generator
-  FoamX->Initialize();        // Initialize simulator, takes a few seconds...
- 
-  for(Long_t loop=0; loop<100000; loop++){
-    FoamX->MakeEvent();          // generate MC event
-    //FoamX->GetMCvect( MCvect);   // get generated vector (x,y)
-    //Double_t x=MCvect[0];
-    //Double_t y=MCvect[1];
-    //if(loop<10) cout<<"(x,y) =  ( "<< x <<", "<< y <<" )"<<endl;
-    // hst_xy->Fill(x,y);           // fill scattergram
-  }
-  Double_t mcResult, mcError;
-  FoamX->GetIntegMC(mcResult,mcError);  // get MC integral, should be one
-  cout<<"wartosc= "<<mcResult<<" ("<<mcError<<")"<<endl;
-}
-
-double fsubg(double x)
-{
-  double a=2.*(exp(-0.5)/sqrt(2*TMath::Pi())-1.);
-  double b=2.-exp(-0.5)/sqrt(2*TMath::Pi());
-  // double a=-1.516;
-  //double b=1.758;
-  double f=(exp(-x*x/2.))/sqrt(2.*TMath::Pi());
-  double g=a*x+b;
-  return (f-g);
-}
-
-double f(double x)
-{
-  return (exp(-x*x/2.))/sqrt(2.*TMath::Pi());
-}
-void ZA(int n, double * wyniki)
-{
-
-  if(wyniki==NULL){return;}
-  // double a=2.*(exp(-0.5)/sqrt(2*TMath::Pi())-1.);
-  //double b=2.-exp(-0.5)/sqrt(2*TMath::Pi());
-  double wartosc=0.; 
-  double sigma=0.;
-  double *wartf=new double[n];
-  double x;
-  for(int i=0;i<n;++i)
-    {
-      x=gRandom->Rndm();
-      wartf[i]=(f(x)+f(1.-x))/2.;
-    }
-  for(int i=0;i<n;++i)
-    {
-      wartosc+=wartf[i];
-    }
-  wartosc/=(double)n;
-  for(int i=0;i<n;++i)
-    {
-      sigma+=pow((wartf[i]-wartosc),2.);
-    }
-  sigma/=(double)(n-1.);
-  sigma=sqrt(sigma/(double)n);
-  wyniki[0]=wartosc;
-  //  cout<<2*(double)n/trafienia<<endl;
-  wyniki[2]=sigma;
-  wyniki[1]=wartosc-0.34134474606854294859;
-}
-
-void MZK(int n, double * wyniki)
-{
-
-  if(wyniki==NULL){return;}
-  double a=2.*(exp(-0.5)/sqrt(2*TMath::Pi())-1.);
-  double b=2.-exp(-0.5)/sqrt(2*TMath::Pi());
-  double wartosc=0.; 
-  double sigma=0.;
-  double *wartf=new double[n];
-  double x;
-  for(int i=0;i<n;++i)
-    {
-      x=gRandom->Rndm();
-      wartf[i]=fsubg(x);
-    }
-  for(int i=0;i<n;++i)
-    {
-      wartosc+=wartf[i];
-    }
-  wartosc/=(double)n;
-  for(int i=0;i<n;++i)
-    {
-      sigma+=pow((wartf[i]-wartosc),2.);
-    }
-  sigma/=(double)(n-1.);
-  sigma=sqrt(sigma/(double)n);
-  wyniki[0]=wartosc+0.5*a+b;
-  //  cout<<2*(double)n/trafienia<<endl;
-  wyniki[2]=sigma;
-  wyniki[1]=wartosc-0.34134474606854294859;
-}
-
-double generatorG()
-{
-  double q;//q=(gRandom->Rndm());
-  double P;//P=(exp(-0.5)-1)*q*q/(2*sqrt(2*TMath::Pi()))+q/(2*sqrt(2*TMath::Pi()));
-  double a=2.*(exp(-0.5)/sqrt(2*TMath::Pi())-1.);
-  double b=2.-exp(-0.5)/sqrt(2*TMath::Pi());
-  while(1)
-    {
-     
-      q=gRandom->Rndm();
-      //    P=(exp(-0.5)-1)*q*q/(2*sqrt(2*TMath::Pi()))+q/(2*sqrt(2*TMath::Pi()));
-      P=a*q*q/2.+b*q;
-      //   if((gRandom->Rndm()*(1+exp(-0.5))/(2*sqrt(2*TMath::Pi())))<P)
-      if(gRandom->Rndm()<P)
-	{
-	  return q;
-	}
-    }
- 
-}