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In probability theory and statistics, the empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, [1] i.e. by means not of a theoretical sample space but of an actual experiment.
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one.
This is the same as saying that the probability of event {1,2,3,4,6} is 5/6. This event encompasses the possibility of any number except five being rolled. The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty.
Static vs. dynamic. A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models typically are represented by differential equations or difference equations. Explicit vs. implicit.
The probability of the event that the sum + is five is , since four of the thirty-six equally likely pairs of outcomes sum to five. If the sample space was all of the possible sums obtained from rolling two six-sided dice, the above formula can still be applied because the dice rolls are fair, but the number of outcomes in a given event will vary.
Epistemic or subjective probability is sometimes called credence, as opposed to the term chance for a propensity probability. Some examples of epistemic probability are to assign a probability to the proposition that a proposed law of physics is true or to determine how probable it is that a suspect committed a crime, based on the evidence ...
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