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Program 1

Coin Tossing Simulation

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

Output 1

Program 2

Coin Tossing Simulation

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

Output 2

Program 3

Coin Tossing Simulation

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

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()

Output 3

Program 4

Coin Tossing Simulation

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

Output 4

Application in Statistical Mechanics

Coin Tossing Simulation

Coin Tossing Simulation

Coin Tossing Simulation

Coin Tossing Simulation