Use python to:

(1) Familiarize with the given code:

(i) Inspection of the code

(ii) Identify where the missing code is to complete the calculation of pi

(2) Complete the code to calculate pi

(i) Add a block to count how many points inside the circile

(ii) Play with your code to calculate pi by changing the parameters, i.e., how many points you generate

(iii) Are there any points right on the boundaries?

code to start:

import sys

import numpy as np # an alias for the namespace

import random

import matplotlib.pyplot as plt

#setting MC parameters

NumP=10000 # generate how many random point in side the square

#MC simulation block

pi_all=[]

cordx=[];cordy=[] # initialize the two empty coordinate lists

inside=0

for i in range(0,NumP): #generate random coordinates

cordx.append(random.random())

cordy.append(random.random())

r2 = cordx[i]*cordx[i]+cordy[i]*cordy[i]

# write control to count inside

pit= 4.0*inside/NumP

#End of sampling

pi_all.append(pit)

#print out result

print(' ')

print("pi: ","{:10.6f}".format(pit))

plt.hist(pi_all) # print hist of the sampling

# plot the random pair: cordx,cordy graphically for the last MC simulation

Symbol=10

LineW = 3

Lsp=100

f = plt.figure()

f.set_figwidth(8)

f.set_figheight(8)

plt.xlim(0,1)

plt.ylim(0,1)

plt.xlabel('X Cordinate')

plt.ylabel('Y Cordinate')

plt.scatter(cordx, cordy, s=Symbol,marker='o')

#plot circle

x = np.linspace(0,1,Lsp)

y = np.sqrt(1. - x*x)

plt.plot(x, y,'-r',color='red', linestyle='-', lw=LineW)

plt.show()