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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.
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.
An operational definition is designed to model or represent a concept or theoretical definition, also known as a construct.Scientists should describe the operations (procedures, actions, or processes) that define the concept with enough specificity such that other investigators can replicate their research.
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.
The application of theoretical sampling provides a structure to data collection as well as data analysis. It is based on the need to collect more data to examine categories and their relationships and assures that representativeness exists in the category. [5] Theoretical sampling has inductive as well as deductive characteristics. [6]
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [12] by Abraham Wald in the context of sequential tests of statistical hypotheses. [13]
A discrete probability distribution is the probability distribution of a random variable that can take on only a countable number of values [15] (almost surely) [16] which means that the probability of any event can be expressed as a (finite or countably infinite) sum: = (=), where is a countable set with () =.
There are also evidential interpretations of probability covering groups, which are often labelled as 'intersubjective' (proposed by Gillies [14] and Rowbottom). [6] Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing.