## tc

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.