15. Geometric

The geometric distribution applies when an experiment is run repeatedly until a successful outcome occurs, and the probability of a success is the same for all trials. The random variable could be defined as the number of fails till the first success, and has a range of integers zero and above. The random variable could also be labeled as the number of trials till the first success and the range is integers one and above. Both scenarios are described in the chapter. This situation occurs, for example, when a process produces units that need to meet acceptable engineering standards, and the process is repeated until an acceptable unit is produced. When the probability of a successful outcome is not known, sample data can be used to estimate the probability. Sometimes, no sample data is available, and a person of experience offers an approximation on the distribution and this data is used to estimate the probability of a successful outcome. The chapter also describes how the geometric distribution is the only discrete distribution that has a memory less property.