Binomial Distribution

It is time to figure out what Binomial distribution is.

To work with this distribution, we should import the binom object from scipy.stats, and then you can apply numerous functions to this distribution like pmf, sf, and cdf that were already learned.

Key characteristics:

This distribution is the same as the Bernoulli distribution, which is repeated several times.

Example:

Tossing a coin is a Bernoulli distribution, but tossing one coin 3 times creates a binomial distribution.

binomial

By the way, Y-axis defines the probability in percents, for the better understanding(in this chapter and the next).

Do you remember the function .cdf()? The function shows the probability of having k or fewer successes among n trials with the defined probability p. It is time to recall it!

Taak

Swipe to start coding

Imagine you passing a test that includes 12 questions; there are just two answers for each question (one of them is correct, another isn't correct). The probability of getting the right answer is 50% or 0.5. Here is the distribution:

binom

You have excellent marks, and you know that if you receive less than 6 or exactly 7 points, you will spoil it.

Import binom object.
Calculate the probability of receiving 6 or less points in the test where the probability of answering right is 0.5 and the number of questions is 12.
Calculate the probability of receiving exactly 7 points in the test where the probability of answering right is 0.5 and the number of questions is 12.
Calculate the whole probability.

Oplossing

# Import binom object

from scipy.stats import binom

import numpy as np

np.random.seed(2000)

# Calculate the first probability

prob_1 = binom.cdf(k = 6, n = 12, p = 0.5)

# Calculate the second probability

prob_2 = binom.pmf(k = 7, n = 12, p = 0.5)

# Calculate the whole probability

prob = prob_1 + prob_2

# Print the probability

print("The probability is", prob)

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Sectie 4. Hoofdstuk 4

# Import binom object

from scipy.___ import ___