coffee cup problem.ipynb

Kernel: Python 3 (system-wide)

import random as r
from numba import njit
import numpy as np
import matplotlib.pyplot as plt

# returns how many pours it took to fill the cup

@njit
def fill_the_cup():
    cup = 0
    pours = 0
    while cup < 1:
        cup += r.uniform(0,1)
        pours += 1
    return pours

runs = 10_000_000

results = np.zeros(15)

for k in range(runs):
    results[fill_the_cup()] += 1

plt.ylabel('Frequency');
plt.xlabel('pours');
plt.bar(range(len(results)), results, 1/1.5, color="blue");
plt.show()

$\overline{\text{necessary pours}}=\sum_k [k \times (\text{proportion of time need k pours})]$

(np.array(range(15)) @ results)/runs

2.7184591