Cara menggunakan binomial distribution in python

Discrete Distribution:The distribution is defined at separate set of events, e.g. a coin toss's result is discrete as it can be only head or tails whereas height of people is continuous as it can be 170, 170.1, 170.11 and so on.

Example

Given 10 trials for coin toss generate 10 data points:

from numpy import random

x = random.binomial(n=10, p=0.5, size=10)

print(x)

Visualization of Binomial Distribution

Example

from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns

sns.distplot(random.binomial(n=10, p=0.5, size=1000), hist=True, kde=False)

plt.show()

Result

Difference Between Normal and Binomial Distribution

The main difference is that normal distribution is continous whereas binomial is discrete, but if there are enough data points it will be quite similar to normal distribution with certain loc and scale.

If a random variable X follows a binomial distribution, then the probability that X = k successes can be found by the following formula:

P(X=k) = nCk * pk * (1-p)n-k

where:

• n: number of trials
• k: number of successes
• p: probability of success on a given trial
• nCk: the number of ways to obtain k successes in n trials

This tutorial explains how to use the binomial distribution in Python.

How to Generate a Binomial Distribution

You can generate an array of values that follow a binomial distribution by using the random.binomial function from the numpy library:

from numpy import random

#generate an array of 10 values that follow a binomial distribution
random.binomial(n=10, p=.25, size=10)

array([5, 2, 1, 3, 3, 3, 2, 2, 1, 4])

Each number in the resulting array represents the number of “successes” experienced during 10 trials where the probability of success in a given trial was .25.

How to Calculate Probabilities Using a Binomial Distribution

You can also answer questions about binomial probabilities by using the binom function from the scipy library.

Question 1: Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes exactly 10?

from scipy.stats import binom

#calculate binomial probability
binom.pmf(k=10, n=12, p=0.6)

0.0639

The probability that Nathan makes exactly 10 free throws is 0.0639.

Question 2: Marty flips a fair coin 5 times. What is the probability that the coin lands on heads 2 times or fewer?

from scipy.stats import binom

#calculate binomial probability
binom.cdf(k=2, n=5, p=0.5)

0.5

The probability that the coin lands on heads 2 times or fewer is 0.5.

Question 3: It is known that 70% of individuals support a certain law. If 10 individuals are randomly selected, what is the probability that between 4 and 6 of them support the law?

from scipy.stats import binom

#calculate binomial probability
binom.cdf(k=6, n=10, p=0.7) - binom.cdf(k=3, n=10, p=0.7)

0.3398

The probability that between 4 and 6 of the randomly selected individuals support the law is 0.3398.

How to Visualize a Binomial Distribution

You can visualize a binomial distribution in Python by using the seaborn and matplotlib libraries:

from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns

x = random.binomial(n=10, p=0.5, size=1000)

sns.distplot(x, hist=True, kde=False)

plt.show()

The x-axis describes the number of successes during 10 trials and the y-axis displays the number of times each number of successes occurred during 1,000 experiments.