### Definition(s)

#### Marginal Probability

Statistical distribution (probability) of the occurrence of a variable A that is obtained by integrating over all values of the other variables *B, C,* …

NOTE The marginal probability of *A* for all values of *B, C,* … is written as *P(A)*. The concept is applicable to metocean parameters, as well as to actions and action effects.

EXAMPLE When considering wave conditions, A can be the individual crest elevation for all mean zero-crossing periods *B* and all significant wave heights *C*, occurring at a particular site.

*Source: API RP 2MET, Derivation of Metocean Design and Operating Conditions, First Edition, November 2014. Global Standards*

#### Marginal Probability

Marginal probability is the unconditional probability of event A, P(A). It is the probability of A regardless of whether event B did or did not occur. If B can be thought of as the event of a random variable X having a given outcome, then the marginal probability of A can be obtained by summing (or integrating, more generally) the joint probabilities over all outcomes for X.

**Sample Usage:** Analysts estimated the marginal probability of a water system contamination, irrespective of the source or type of contaminate.

*Source: DHS Risk Lexicon, U.S. Department of Homeland Security, 2010 Edition. September 2010 Regulatory Guidance*