// chi^2-Test: ist Wuerfel gezinkt?
void wuerfel()
{
  const int NBINS = 6;
  const int N     = 100;   // 100x wuerfeln
  const int NPE   = 1000;
  const double p  = 1./6.;
  double pi = N*p;

  TH1* h = new TH1F( "h", "Gezinkter Wuerfel?", 6, 0.5, 6.5 );
  h->SetMinimum( 0 );
  h->SetStats( kFALSE );

  TH1* href = new TH1F( "href", "Referenzhistogramm", 6, 0.5, 6.5 );
  for( int i = 1; i <= NBINS; ++i ) {
    href->SetBinContent( i, pi );
    href->SetBinError( i, 0 );
  }

  TH1* hpe = new TH1F( "hpe", "#chi^{2}-Pruefgroesse", 30, 0, 15 );
  TH1* hprob = new TH1F( "hprob", "#chi^{2}-Wahrscheinlichkeit", 20, 0, 1 );
  hprob->SetMinimum( 0 );

  for( int ipe = 0; ipe < NPE; ++ipe ) {
    h->Reset();
    for( int i = 0; i < N; ++i ) {
      // nicht gezinkt
      h->Fill( gRandom->Integer( NBINS ) + 1 );

      // gezinkt: jedes 10x Mal eine 6
      // if( ( i % 10 ) == 0 ) h->Fill( 6 );
      // else h->Fill( gRandom->Integer( NBINS ) + 1 );

      // gezinkt: 60% nicht zufaellig
      // switch( i % 10 ) {
      // case 1: h->Fill( 1 ); break;
      // case 2: h->Fill( 2 ); break;
      // case 3: h->Fill( 3 ); break;
      // case 4: h->Fill( 4 ); break;
      // case 5: h->Fill( 5 ); break; 
      // case 6: h->Fill( 6 ); break;
      // default:  h->Fill( gRandom->Integer( NBINS ) + 1 );
      // }
    }
    if( ipe == 0 ) {
      h->Draw();
      gPad->SaveAs( "wuerfel.pdf" );
    }
    double chi2 = 0;
    for( int i = 1; i <= NBINS; ++i ) {
      chi2 += pow( h->GetBinContent( i ) - pi, 2) / pi;
    }
    cout << "chi2: " << chi2 << endl;
    cout << "TH1::Chi2Test: ";
    double prob = h->Chi2Test( href, "P" ); 
    cout << endl;
    hpe->Fill( chi2 );
    hprob->Fill( prob );
  }
  hpe->Draw();
  gPad->SaveAs( "wuerfel_chi2.pdf" );

  hprob->Draw();
  gPad->SaveAs( "wuerfel_chi2_prob.pdf" );
}