Binomial Distribution
Overview
- The Binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials.
- Each trial has two possible outcomes: success or failure.
Use Case
- Used when conducting a fixed number of independent trials with two possible outcomes in each trial, such as flipping a coin a certain number of times or conducting a series of yes/no experiments.
- Probability Mass Function (PMF):$$
P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k}
Example
- Coin Flipping:
- Suppose we flip a fair coin 5 times (( n = 5 )).
- Let ( p = 0.5 ) (fair coin).
- We want to find the probability of getting exactly 3 heads (( k = 3 )).
- Using the Binomial PMF:
