What is the primary difference between a binomial model and a negative binomial model regarding what is fixed and what is counted?

Conditions

• Trials are independent.
• Success probability is constant.

Reasoning, step by step

1. Identify the fixed parameter in a binomial model: the total number of trials.
2. Identify the random variable in a binomial model: the count of successes.
3. Identify the fixed parameter in a negative binomial model: the target number of successes.
4. Identify the random variable in a negative binomial model: the count of trials needed.

Example

The script states: 'A binomial model fixes the number of trials and counts successes. Here the negative binomial variable instead counts the trials needed to reach r successes.'

Common misconceptions

• Thinking both models fix the number of trials.
• Confusing the random variable (successes vs. trials) between the two models.

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Connected concepts

Explore next

• How is the probability mass function for the negative binomial derived?
• What is the mean of the negative binomial distribution under the total-trials convention?