The Poisson distribution 57 The negative binomial distribution The negative binomial distribution is a generalization of the geometric [and not the binomial, as the name might suggest]. Let us ﬁx an integer) ≥ 1; then we toss a!-coin until the)th heads occur. Let X) denote the total number of tosses. Example 4 (The negative binomial. The above form of the Geometric distribution is used for modeling the number of trials until the first success. The number of trials includes the one that is a success: x = all trials including the one that is a success. This can be seen in the form of the formula. The geometric distribution describes the probability of experiencing a certain amount of failures before experiencing the first success in a series of Bernoulli trials. A Bernoulli trial is an experiment with only two possible outcomes - "success" or "failure" - and the probability of success is the same each time the experiment is conducted. Probability distribution for a geometric distribution don't add up to 1 Say I'm rolling 2 dies, numbered 1 to 10. A successful outcome is considered rolling a multiple of 4. Therefore, probability of success = 0.25 and prob of failure = 0.75. This is an example of a geometric distribution. I can roll a maximum of 6 times.