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In probability theory, the sample space (also called sample description space, [1] possibility space, [2] or outcome space [3]) of an experiment or random trial is the set of all possible outcomes or results of that experiment. [4] A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, [5] are ...
e. In probability theory, a probability space or a probability triple is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die . A probability space consists of three elements: [1] [2] A sample space, Ω {\displaystyle \Omega }
Definition. A random variable is a measurable function from a sample space as a set of possible outcomes to a measurable space . The technical axiomatic definition requires the sample space to be a sample space of a probability triple (see the measure-theoretic definition ). A random variable is often denoted by capital Roman letters such as .
e. In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
Probability theory. Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability ...
The law of total probability is [1] a theorem that states, in its discrete case, if is a finite or countably infinite set of mutually exclusive and collectively exhaustive events, then for any event : or, alternatively, [1] where, for any , if , then these terms are simply omitted from the summation since is finite.
t. e. In probability theory, an outcome is a possible result of an experiment or trial. [1] Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space. [2]
In probability theory, an elementary event, also called an atomic event or sample point, is an event which contains only a single outcome in the sample space. [1] Using set theory terminology, an elementary event is a singleton. Elementary events and their corresponding outcomes are often written interchangeably for simplicity, as such an event ...