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A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. [1] The term 'random variable' in its mathematical definition refers to neither randomness nor variability [ 2 ] but instead is a mathematical function in which
Formally, a multivariate random variable is a column vector = (, …,) (or its transpose, which is a row vector) whose components are random variables on the probability space (,,), where is the sample space, is the sigma-algebra (the collection of all events), and is the probability measure (a function returning each event's probability).
A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness .
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.
R is a programming language for statistical computing and data visualization. It has been adopted in the fields of data mining, bioinformatics and data analysis. [9] The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data. R software is open-source and free software.
Criterion Validity is correlation between the test and a criterion variable (or variables) of the construct. Regression analysis, Multiple regression analysis, and Logistic regression are used as an estimate of criterion validity. Software applications: The R software has ‘psych’ package that is useful for classical test theory analysis. [6]
The reverse correlation technique is a data driven study method used primarily in psychological and neurophysiological research. [1] This method earned its name from its origins in neurophysiology, where cross-correlations between white noise stimuli and sparsely occurring neuronal spikes could be computed quicker when only computing it for segments preceding the spikes.
In the early 1930s, Aleksandr Khinchin gave the first mathematical definition of a stochastic process as a family of random variables indexed by the real line. [ 25 ] [ 22 ] [ a ] Further fundamental work on probability theory and stochastic processes was done by Khinchin as well as other mathematicians such as Andrey Kolmogorov , Joseph Doob ...