Basic Concepts of Probability and Statistics in the Law by Michael O. Finkelstein

Author:Michael O. Finkelstein
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

The Geometric and Exponential Distributions

Many problems in the law relate to how long someone, or something, will live (or last). When there is a series of discrete independent trials, with probability p of failure on each trial, the probability distribution of the number of trials to the first failure is described by what is called the geometric distribution. In trials with a geometric distribution, the mean number of such trials is given by 1/p. Thus, if there is a 5% chance of failure on a single trial, the mean number of trials to failure is 20. Unlike the distributions discussed thus far, there is no “bunching” of probability around the mean number. In fact, the single result with the greatest probability of failure is not the mean number of trials but the first trial. See Fig. 5.3.

Fig. 5.3Probability density function for the standard exponential distribution

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