A company offers a free trial of its products for 7 days. It was observed that on average 2 out of 10 products sold are returned. Using Poisson, find the probabilities of the following event: exactly 6 products out of 40 sold are being returned.

Using the previous equation to compute the probabilities, and considering that if 2 out of 10 are returned, then λ in 40 are returned. Therefore, λ = 8 returned products and:

• Find exactly six products that should return:

p(x = 6) = 0.1221.

from scipy.stats import poisson

import matplotlib.pyplot as plt

import numpy as np

mu = 0.6

x = np.arange(0, 20, 1)

y = poisson.pmf(x, mu)

plt.plot(x,y,'r-',x, y,'bo')

plt.show()

from scipy.stats import binom

import matplotlib.pyplot as plt

import numpy as np

# computing P(X) for each X.

x = [0, 1, 2, 3, 4, 5, 6]

mu = 8

y = poisson.pmf(x, mu)

print('  X  |',x)

print('P(X) |',y)

   X | [0, 1, 2, 3, 4, 5, 6] 

P(X) | [0.00033546 0.0026837 0.0107348 0.02862614 0.05725229 0.09160366 0.12213822]