Question

Consider flipping nn times a coin. The probability for heads is given by pp where pp is some parameter which can be chosen from the interval (0,1)(0,1).

Write a Python code to simulate nn coin flips with heads probability pp and compute the running proportion of heads X¯nX¯n for nn running from 1 to 1,000 trials. Plot your results. Your plot should illustrate how the proportion of heads appears to converge to pp as nn approaches 1,000.

In [ ]:

### Insert your code here for simulating the coin flips and for computing the average

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In [2]:

### Complete the plot commands accordingly for also plotting the computed running averages in the graph below

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p = 0.25 # just an example

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plt.figure(figsize=(10,5))

plt.title("Proportion of heads in 1,000 coin flips")

plt.plot(np.arange(1000),p*np.ones(1000),'-',color="red",label="true probability") 

plt.xlabel("Number of coin flips")

plt.ylabel("Running average")

plt.legend(loc="upper right")

Answer 1

The R code for simulating the coin toss is given below. The probability of heads is set at p = 0.25.

You can change the value as you want. The plot shows the probability converges to p = 0.25 as sample size increases.

import matplotlib.pyplot as plt
import numpy as np
def proportion(seed,n, p):
        np.random.seed(seed)
        h = 0
        for i in range(n):
             r = np.random.random_sample(1)
             if(r<p):
                h = h+1
        return(h/n)
N = 1000
p = 0.25
PH = []
seed = 154
for i in range(1,N):
   ph = proportion(seed,i, p)
   PH.append(ph)
if __name__ == "__main__":
    plt.figure(figsize=(10,5))
    plt.title("Proportion of heads in 1,000 coin flips")
    plt.plot(range(1,N),PH,'-',color="red",label="True probability")
    plt.xlabel("Number of coin flips")
    plt.ylabel("Running average")
    plt.legend(loc="upper right")
    plt.show()

Kindly upvote.