Question

You just picked up a coin and is wondering if the coin is truly unbiased. To determine if this coin is unbiased, you decide to do an experiment by flipping this coin 100 times and record how many times it returns head. Let us say this is flipping experiment No.1, and its result is the no. of heads. Then you decide to repeat this flipping experiment 999 more times (for a total of 1000 experiments, in each experiment you flip the coin 100 times).

• Write a function called simulation_coinflip(p) returns a numpy array result with shape (1000,) where the ?i-th element (result[i-1]) in this array is the result of the ?i-th flipping test (the no. of heads in a given flip test).
• Plot the histograms of this array using 50 bins using the resulting array of simulation_coinflip(p) for ?=0.2,0.5,0.7p=0.2,0.5,0.7.
• Remark: using for loops is okay, the code for this problem can be formulated using completely vectorized routines without any for loops, and you MAY or MAY NOT find np.vectorize() (vectorize a function if there is if-else conditionals), np.mean(), np.sum(), np.apply_along_axis, np.count_nonzero(), and np.random.random() useful.

Answer 1

All the explanation is in the code comments. Hope this helps!

Code:

# imports
import numpy as np
import random
import matplotlib.pyplot as plt

# the required function
def simulation_coinflip(p):
  
# number of experiments
n = 1000
result = np.zeros(n)
  
# for 1000 experiments
for i in range(n):
# each experiment is for 100 times
for j in range(100):
  
# check if it is a head
if(random.random() <= p):
result[i] = result[i] + 1
  
# return result
return result

# call the simulation_coinflip() function
result1 = simulation_coinflip(0.2)
result2 = simulation_coinflip(0.5)
result3 = simulation_coinflip(0.7)
plt.hist([result1, result2, result3], bins=50)
plt.xlabel('Number of heads')
plt.ylabel('Number of times')
plt.legend(['p=0.2', 'p=0.5', 'p=0.7'])
plt.show()

Sample run:

Code screenshots: