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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
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.
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 .
A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
If two variables are uncorrelated, there is no linear relationship between them. Uncorrelated random variables have a Pearson correlation coefficient, when it exists, of zero, except in the trivial case when either variable has zero variance (is a constant). In this case the correlation is undefined.
In more formal probability theory, a random variable is a function X defined from a sample space Ω to a measurable space called the state space. [2] [a] If an element in Ω is mapped to an element in state space by X, then that element in state space is a realization.
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]
Several random variables and probability distributions beside the Bernoullis may be derived from the Bernoulli process: The number of successes in the first n trials, which has a binomial distribution B(n, p) The number of failures needed to get r successes, which has a negative binomial distribution NB(r, p)