Introduction to Python Binomial Distribution
Python Binomial Distribution
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials.
A Bernoulli trial is an experiment with two possible outcomes: success or failure, usually denoted as 1 or 0.
The probability mass function (PMF) of the binomial distribution is given by the following formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of getting exactly k successes in n trials.
- C(n, k) is the binomial coefficient, also known as "n choose k," which represents the number of ways to choose k successes from n trials. It is calculated as C(n, k) = n! / (k! * (n - k)!), where ! denotes the factorial function.
- p is the probability of success in a single trial.
- (1 - p) is the probability of failure in a single trial.
- k is the number of successes.
- n is the total number of trials.
In Python, you can use the scipy.stats.binom module from the SciPy library to work with the binomial distribution.
- The
binom.pmf()function can be used to calculate the probability mass function for a specific value of k.
As an example:
from scipy.stats import binom
# Define the parameters
n = 10 # Number of trials
p = 0.5 # Probability of success
# Calculate the probability of getting exactly k successes
k = 3
probability = binom.pmf(k, n, p)
print("Probability of getting exactly", k, "successes:", probability)
In this example:
- We use the
binom.pmf(k, n, p)function to calculate the probability of getting exactly 3 successes in 10 trials, where the probability of success in each trial is 0.5. The result is stored in the variableprobabilityand printed.