The Negative Binomial distribution is a discrete probability distribution that models the number of trials needed to achieve a fixed number of successful outcomes (often referred to as "successes"). It is commonly used in scenarios where we are interested in the number of failures that occur before a certain number of successes is achieved. ### Key Characteristics: 1. **Parameters**: The Negative Binomial distribution is defined by two parameters: - \( r \): the number of successes (a positive integer).
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On the failures-before-the-th-success convention, a negative binomial variable with success probability has probability mass functionIt has expected value and variance .