bernoulli

A Bernoulli experiment is a random experiment that satisfies the following conditions:

Two Possible Outcomes: Each trial has exactly two possible outcomes: “success” or “failure”.
Independence: The trials are independent; the outcome of one trial does not affect the outcome of another.
Constant Probability: The probability of success, $p$, remains constant across all trials.

Examples of Bernoulli experiments include flipping a coin (heads or tails), checking if a light bulb works (works or doesn’t work), or rolling a die to see if it shows a 6 (shows 6 or doesn’t). A sequence of Bernoulli experiments is often called a “Bernoulli process” and forms the basis for the binomial distribution, where we are interested in the number of successes over a fixed number of trials.