void uniform(int nSum = 10) // parametr: počet čísel x_i v sumě
{
	int nGen = 1e6;	// počet generovaných čísel X = sum x_i

	// U(0,1):
	double mu_x    = 0.5;
	double sigma_x = 1./sqrt(12);

	double mu_y    = nSum * mu_x;
	double sigma_y = sqrt(nSum) * sigma_x;

	TRandom3* rnd  = new TRandom3();
	TH1D* histy    = new TH1D("histy",";y", 200,
						mu_y - 4*sigma_y, mu_y + 4*sigma_y);
	histy->SetLineWidth(2);

	for (int j = 0; j < nGen; j++)
	{
		double y = 0;	// = sum x_i, i = 0, 1, ..., nSum-1

		for (int i = 0; i < nSum; i++)
			y += rnd->Rndm();

		histy->Fill(y);
	}

	TF1* fNorm = new TF1("fNorm","1 / (TMath::Sqrt(2*TMath::Pi())*[2]) * gaus",
					mu_y - 4*sigma_y, mu_y + 4*sigma_y);
	fNorm->SetParameter(0,nGen*histy->GetBinWidth(1)); // 1. parametr = normalizace
	fNorm->SetParameter(1,mu_y);	// 2. parametr = mu Gausiánu
	fNorm->SetParameter(2,sigma_y);	// 3. parametr = sigma Gausiánu

	gStyle->SetOptStat(0);	// neukazuj tabulku entries, mean, RMS
	histy->Draw();
	fNorm->Draw("same");

	TLegend* leg = new TLegend(0.6,0.75,0.9,0.9);
	char str[256];
	sprintf(str,"Sumy %i #it{x} #in U(0,1)",nSum);
	leg->AddEntry(histy, str);
	sprintf(str,"%.2e N(%.2f, %.2f)",nGen*histy->GetBinWidth(1),mu_y,sigma_y);
	leg->AddEntry(fNorm, str);
	leg->Draw();
}

void exponential(int nSum = 10)
{
	int nGen = 1e6;	// počet generovaných čísel y = sum x_i

	// exponenciální (lambda = 1/mu_x):
	double mu_x    = 2.0;
	double sigma_x = mu_x;

	double mu_y    = nSum * mu_x;
	double sigma_y = sqrt(nSum) * sigma_x;

	TRandom3* rnd  = new TRandom3();
	TH1D* histy    = new TH1D("histy",";y", 200,
						mu_y - 4*sigma_y, mu_y + 4*sigma_y);
	histy->SetLineWidth(2);

	for (int j = 0; j < nGen; j++)
	{
		double X = 0;	// = sum x_i, i = 0, 1, ..., nSum-1

		for (int i = 0; i < nSum; i++)
			X += rnd->Exp(mu_x);

		histy->Fill(X);
	}

	TF1* fNorm = new TF1("fNorm","1 / (TMath::Sqrt(2*TMath::Pi())*[2]) * gaus",
					mu_y - 4*sigma_y, mu_y + 4*sigma_y);
	fNorm->SetParameter(0,nGen*histy->GetBinWidth(1));	// 1. parametr = normalizace
	fNorm->SetParameter(1,mu_y);	// 2. parametr = mu Gausiánu
	fNorm->SetParameter(2,sigma_y);	// 3. parametr = sigma Gausiánu

	gStyle->SetOptStat(0);	// neukazuj tabulku entries, mean, RMS
	histy->Draw();
	fNorm->Draw("same");

	TLegend* leg = new TLegend(0.6,0.75,0.9,0.9);
	char str[256];
	sprintf(str,"Sumy %i #it{x} #in exp(#it{#tau} = %.1f)",nSum,mu_x);
	leg->AddEntry(histy, str);
	sprintf(str,"%.2e N(%.2f, %.2f)",nGen*histy->GetBinWidth(1),mu_y,sigma_y);
	leg->AddEntry(fNorm, str);
	leg->Draw();
}

void cauchy(int nSum = 10)
{
	int nGen = 1e6;	// počet generovaných čísel y = sum x_i

	// cauchyho = Breitovo-Wignerovo (střed v 0, pološířka 1):
	double mu_x    = 0.0;
	double sigma_x = 1.0;	// skutečný rozptyl je nekonečný

	double mu_y    = nSum * mu_x;
//	double sigma_y = sqrt(nSum) * sigma_x;
	double sigma_y = nSum * sigma_x;

	TRandom3* rnd  = new TRandom3();
	TH1D* histy    = new TH1D("histy",";y", 200,
						mu_y - 4*sigma_y, mu_y + 4*sigma_y);
	histy->SetLineWidth(2);

	for (int j = 0; j < nGen; j++)
	{
		double X = 0;	// = sum x_i, i = 0, 1, ..., nSum-1

		for (int i = 0; i < nSum; i++)
			X += rnd->BreitWigner(mu_x,sigma_x);

		histy->Fill(X);
	}

	TF1* fNorm = new TF1("fNorm","1 / (TMath::Sqrt(2*TMath::Pi())*[2]) * gaus",
					mu_y - 4*sigma_y, mu_y + 4*sigma_y);
	fNorm->SetParameter(0,nGen*histy->GetBinWidth(1));	// 1. parametr = normalizace
	fNorm->SetParameter(1,mu_y);	// 2. parametr = mu Gausiánu
	fNorm->SetParameter(2,sigma_y);	// 3. parametr = sigma Gausiánu

	gStyle->SetOptStat(0);	// neukazuj tabulku entries, mean, RMS
	histy->Draw();
	fNorm->Draw("same");

	TLegend* leg = new TLegend(0.6,0.75,0.9,0.9);
	char str[256];
	sprintf(str,"Sumy %i #it{x} #in Cauchy(#it{l} = %.1f)",nSum,sigma_x);
	leg->AddEntry(histy, str);
	sprintf(str,"%.2e N(%.2f, %.2f)",nGen*histy->GetBinWidth(1),mu_y,sigma_y);
	leg->AddEntry(fNorm, str);
	leg->Draw();
}

void upf_cv7_clt()
{
	printf("Vyberte druh rozdělení:\n");
	printf("\tU rovnoměrné U(0,1)\n");
	printf("\tE exponenciální, tau = 2\n");
	printf("\tC Cauchyho, l = 1\n");
	char sel = 'u';
	scanf("%1c%*c",&sel);

	printf("Vyberte počet sečtených čísel: ");
	int N = 1;
	scanf("%i%*c",&N);

	if (sel == 'U' || sel == 'u')
		uniform(N);
	else if (sel == 'E' || sel == 'e')
		exponential(N);
	else if (sel == 'C' || sel == 'c')
		cauchy(N);
	else
		printf("Neplatná volba '%c'", sel);
}