Application in Statistical Mechanics - Coin Tossing Simulation

Program 1

Coin Tossing Simulation

Python 3.11 Ready

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

Python program simulates a coin being tossed many times and calculates the probability of getting heads as the number of tosses increases.

Program 2

Coin Tossing Simulation

Python 3.11 Ready

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

Python program simulates a coin being tossed many times and calculates the probability of getting heads as the number of tosses increases.

Program 3

Coin Tossing Simulation

Python 3.11 Ready

from numpy.random import *
from numpy import *
import matplotlib.pyplot as plt
from scipy.special import comb
from scipy.optimize import curve_fit
from scipy.stats import binom, norm
from scipy.integrate import simps
    
Num = 1000         #Number of coin toss expt
n1 = 50      #Number of tossing of coin in each expt
head = []
prob_h = []
h1 = []
hc = [0]*(1+n1)
for n in range(1, Num): 
    recordheads = []
    recordtails = []
    flip = randint(0, 2, n1)

for i in range(n1):
        if (flip[i] == 0):        
            recordheads.append("Heads")
        else:
            recordtails.append("Tails") 
   
    h = recordheads.count("Heads")
    for j in range(n1):
        if (j == h):
            hc[j] = hc[j] + 1
    head.append(h)
    #prob_h.append(probh)
print(hc)
def binm(x, n, p):
    return comb(n1, x)*p**x*(1-p)**(n1-x)
  
plt.title('Fraction of head')
plt.xlim(0, n1)
plt.subplot(121)
plt.hist(head, bins = 10, edgecolor = 'w')
plt.subplot(122)

x1 = []
nrm = []
hcar = asarray(hc)
sum = 0 
for i in range(len(hc)):
    sum = sum + hc[i]
print(sum)
for k in range(len(hc)):
    nrm.append(hc[k]/(sum))
    x1.append(k)
#print(nrm)
plt.plot(x1, nrm, '.')
b = []
x = []
for j in range(0, len(hc), 1):
    b.append(binm(j, n1, 0.5))
    x.append(j)
plt.plot(x, b, '-')
plt.savefig('plot.png') 
plt.show()

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

Analyzing the results of multiple coin toss experiments, calculating the distribution of heads, and comparing it with the theoretical binomial probability distribution.

Program 4

Coin Tossing Simulation

Python 3.11 Ready

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

Analyzing the results of multiple coin toss experiments, calculating the distribution of heads, and comparing it with the theoretical binomial probability distribution.

Ch. 20.3 Coin Tossing Simulation

Coin Tossing Simulation

Mathematical Problem Formulation

Coin Tossing Simulation

Mathematical Problem Formulation

Coin Tossing Simulation

Mathematical Problem Formulation

Coin Tossing Simulation

Mathematical Problem Formulation