The Bernoulli distribution is used to model binary outcomes where there are only two possible results: success or failure. It's characterized by a single parameter p, which represents the probability of success.
📊 What is the Bernoulli Distribution?
Definition: A probability distribution describing outcomes of a single trial where success occurs with probability p and failure with 1−p.
🔍 Bernoulli Trials: Key Characteristics
Single Experiment: Each trial has only two possible outcomes.
Independent Outcomes: The outcome of one trial does not affect the outcome of another.
Two Outcomes: Success and failure are the only possible results.
Constant Probability: p remains constant across all trials.
🌟 Examples of Bernoulli Trials
Coin Toss: Tossing a fair coin where getting heads (success) or tails (failure).
Picking a Card: Drawing a heart from a deck of cards (success) or not drawing a heart (failure).
Free Throw: Making a basket in basketball (success) or missing (failure).
Examples of Bernoulli Trials
📐 Mathematical Explanation
The Bernoulli distribution's PMF calculates the probability of observing k successes in a single trial, where k can be either 0 or 1.
🛠️ How It Works?
Probability Calculation: Determines the likelihood of a specific outcome occurring in a single trial.
Modeling Binary Data: Used extensively in situations where outcomes are binary, such as yes/no or success/failure scenarios.
🌍 When to Use Bernoulli Distribution?
Binary Outcomes: Ideal for modeling outcomes with two categories.
Data Modeling: Used in various statistical analyses and machine learning algorithms.
