n the negative binomial distribution, we have a fixed number of successes, which is usually denoted as r.  How is this different from the binomial distribution?In the negative binomial distribution, we are not interested in the number of trials required to get a certain number of successes.In the binomial distribution, we have a fixed number of trials (say, n), and the independent variable is the number of successes in those n trials.In the binomial distribution, we also have a fixed number of successes, but we are only interested in the probability of the first success.SkipSubmit

The main difference between the negative binomial distribution and the binomial distribution lies in what is being measured.

In a binomial distribution, we have a fixed number of trials, denoted as n, and we are interested in the number of successes within these n trials. The probability of success on each trial is constant and each trial is independent of each other.

On the other hand, in a negative binomial distribution, we are interested in the number of trials required to achieve a fixed number of successes, usually denoted as r. The trials are also independent in this case and the probability of success is constant. However, the number of trials is not fixed and can be any number that is equal to or greater than the number of successes we are interested in.

So, in summary, the binomial distribution is concerned with the number of successes in a fixed number of trials, while the negative binomial distribution is concerned with the number of trials needed to achieve a fixed number of successes.