Programming in C++

ROOT as in the program ROOT developed at CERN

Thank you in advanced

o3. Monte Carlo Integration using ROOT. Use a monte carlo integration program to find the area of a unit circle. (In other words, use Monte Carlo integration to find the value of pi) e You may use symmetry to restrict your calculation to positive x- and y-values. Check the behavior of the program as a function of the number of evaluation points, as follows. o Try the calculation using 100, 1000, 10000 point. o For each of those, you will repeat the calculation 100 times. o Each time, you will obtain the difference between the calculated value of pi and true pi. You will plot these differences in a histogram (TH1D). Hence, 3 histograms, each with 100 entries, for the 3 cases: N 100, 1000, and 10000. o Compare the RMS of each histogram. You should verify that the RMS is reduced as you increase N. What is the behavior of RMS/pi vs N? Predict what should the RMS be for 100,000 points. Discuss with your Lab TA o3. Monte Carlo Integration using ROOT. Use a monte carlo integration program to find the area of a unit circle. (In other words, use Monte Carlo integration to find the value of pi) e You may use symmetry to restrict your calculation to positive x- and y-values. Check the behavior of the program as a function of the number of evaluation points, as follows. o Try the calculation using 100, 1000, 10000 point. o For each of those, you will repeat the calculation 100 times. o Each time, you will obtain the difference between the calculated value of pi and true pi. You will plot these differences in a histogram (TH1D). Hence, 3 histograms, each with 100 entries, for the 3 cases: N 100, 1000, and 10000. o Compare the RMS of each histogram. You should verify that the RMS is reduced as you increase N. What is the behavior of RMS/pi vs N? Predict what should the RMS be for 100,000 points. Discuss with your Lab TA