Geometric distribution

When performing an experiment with only two outcomes, this discrete distribution can model the number of consecutive trials necessary to observe the outcome of interest for the first time. It can also model the number of nonevents that occur before you observe the first outcome. For example, a geometric distribution can model the number of times you must flip a coin to obtain the first "heads" outcome. Similarly, for products built on an assembly line, it can model the number units produced before the first defective unit is produced.

An important property of the geometric distribution is that it is memoryless. The memoryless property states that if the specified outcome has not yet occurred in a series of trials, then the number of past trials in the series does not change the probability distribution of the number of trials remaining before you first observe the specified outcome. In other words, at any point in the series of trials, this probability distribution will be unchanged, as if the past trials had not occurred at all. For example, at the outset of a series of coin tosses, a coin has a certain probability distribution for the number of trials until the first "heads" occurs. If you toss the coin 100 times without observing any "heads", the memoryless property states that the coin will have the same probability distribution for the number of trials remaining until the first "heads" occurs that it possessed at the outset. This distribution remains unchanged throughout the series of trials, as if the past trials has not occurred at all. This property is not applicable to every process, however; a system that experiences wear and tear, and therefore becomes more likely to fail later in its life, is not memoryless.