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For a negative binomial distribution, the mean and variance are related by

Question

For a negative binomial distribution, the mean and variance are related by

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Solution

In a negative binomial distribution, the mean (μ) and variance (σ^2) are related by the following formula:

σ^2 = μ + (μ^2 / k)

where k is the number of successes we are interested in.

This relationship shows that the variance is equal to the mean plus the square of the mean divided by the number of successes. This means that the variance is always greater than or equal to the mean in a negative binomial distribution.

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