chebychev's inequality

import numpy as np
shape, scale = 2., 2.  # mean=4, std=2*sqrt(2)
mu = shape*scale
sigma = scale*np.sqrt(shape)
s = np.random.normal(shape, scale, 1000000)

import random
# sample 10000 sample
rs = random.choices(s, k=10000)

ks = [0.1,0.5,1.0,1.5,2.0,2.5,3.0]
# prob list
probs = []
# for each k
for k in ks: 
    # start count
    c = 0
    # for each data sample
    for i in rs:
        # count if far from mean in k standard deviation
        if abs(i - mu) > k * sigma :
            c += 1
    # count divided by number of sample
    probs.append(c/10000)
    
import matplotlib.pyplot as plt
# set figure size
plt.figure(figsize=(20,10))
# plot each probability
plt.plot(ks,probs, marker='o')
# show plot
plt.show()
# print each probability
print("Probability of a sample far from mean more than k standard deviation:")
for i, prob in enumerate(probs):
    print("k:" + str(ks[i]) + ", probability: " \
          + str(prob)[0:5] + \
          " | in theory, probability should less than: " \
          + str(1/ks[i]**2)[0:5])