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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]
(Likelihoods are comparable, e.g. for parameter estimation, only if they are Radon–Nikodym derivatives with respect to the same dominating measure.) The above discussion of the likelihood for discrete random variables uses the counting measure, under which the probability density at any outcome equals the probability of that outcome.
In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable additivity. [1] The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume ) is that a probability measure must ...
The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration.
A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
A simple example is a volume (how big an object occupies a space) as a measure. In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and ...
The goal of logistic regression is to use the dataset to create a predictive model of the outcome variable. As in linear regression, the outcome variables Y i are assumed to depend on the explanatory variables x 1,i... x m,i. Explanatory variables. The explanatory variables may be of any type: real-valued, binary, categorical, etc.
A probability distribution is a function that assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.