#
# Blatt 9 Aufgabe 9.2
#
# Test zentraler Grenzwertsatz der Statistik
# sum uniformly distributed random numbers
# and histogramm them. 
#
# To be used with pyRoot
#
import ROOT
import math

# number of events 
nEvent = 50000
  
# Create a new canvas, and customize it.
c1 = ROOT.TCanvas( 'c1', 'Zentraler Grenzwertsatz', 200, 10, 700, 500 )
c1.Divide(2,3)

# Initialize random number generator
R = ROOT.TRandom3()
# R.SetSeed(7892344)  # fixed seed for testing
R.SetSeed()  # set seed to machine clock
  
# Create Histogramms
x1  = ROOT.TH1D( 'x1', 'n=1', 500, 0., 10)
x2  = ROOT.TH1D( 'x2', 'n=2', 500, 0., 10)
x3  = ROOT.TH1D( 'x3', 'n=3', 500, 0., 10)
x6  = ROOT.TH1D( 'x6', 'n=6', 500, 0., 10)
x8  = ROOT.TH1D( 'x6', 'n=8', 500, 0., 10)
x10  = ROOT.TH1D( 'x6', 'n10',500, 0., 10)

# Event loop
for i in range(nEvent) :
  # random numbers between 0 and 1
  # Filling histogramm with sums of uniformly distributed random numbers
  # The sums are with the increasing numbers of random variables more
  # and more gaussian
  n1 = R.Uniform(0.,1)
  x1.Fill(n1)
  n2 = R.Uniform(0.,1)
  x2.Fill(n1+n2)
  n3 = R.Uniform(0.,1)
  x3.Fill(n1+n2+n3)
  n4 = R.Uniform(0.,1)
  n5 = R.Uniform(0.,1)
  n6 = R.Uniform(0.,1)
  x6.Fill(n1+n2+n3+n4+n5+n6)
  n7 = R.Uniform(0.,1)
  n8 = R.Uniform(0.,1)
  x8.Fill(n1+n2+n3+n4+n5+n6+n7+n8)  
  n9 = R.Uniform(0.,1)
  n10 = R.Uniform(0.,1)
  x10.Fill(n1+n2+n3+n4+n5+n6+n7+n8+n9+n10)  
# Draw histogramms and fit gaussian distributions  
c1.cd(1)
x1.Draw()
c1.cd(2)
x2.Draw()
x2.Fit('gaus')
c1.cd(3)
x3.Draw()
x3.Fit('gaus')
c1.cd(4)
x6.Draw()
x6.Fit('gaus')
c1.cd(5)
x8.Draw()
x8.Fit('gaus')
c1.cd(6)
x10.Draw()
x10.Fit('gaus')

c1.Draw()

c1.Modified()
c1.Update()