中心極限定理を確かめて遊んでみた。(script for ROOT)

central_limit_theorem.cc

// 中心極限定理を確かめて遊んでみた。(script for ROOT)
{
  int n = 10000;
  int m = 2;
  int nbin = 100;
  double limit = 8.0;
  double binwidth = 2.0*limit/double(nbin);

  TH1D *h = new TH1D("h", "hist", nbin, - limit, limit);

  
  double x;
  for (int i = 0; i < n; i++){
    x = 0;
    for (int j = 0; j < m; j++){
      x += gRandom->Uniform(0, 1);
    }
    h->Fill((x/double(m) - 0.5) * sqrt(m)*sqrt(12.0));
  }
  
  h->Draw();

  TF1 *f = new TF1("f","gaus(0)", -10, 10);
  f->SetParameters(double(n)*binwidth/sqrt(TMath::TwoPi()), 0, 1.0);
  f->Draw("same");

}