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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
The number of dummy variables is always one less than the number of categories: with the two categories black and white there is a single dummy variable to distinguish them, while with the three age categories two dummy variables are needed to distinguish them. Such qualitative data can also be used for dependent variables. For example, a ...
The definition extends naturally to more than two random variables. We say that n {\displaystyle n} random variables X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}} are i.i.d. if they are independent (see further Independence (probability theory) § More than two random variables ) and identically distributed, i.e. if and only if
In this example, the "lurking" variable (or confounding variable) causing the paradox is the size of the stones, which was not previously known to researchers to be important until its effects were included. [citation needed] Which treatment is considered better is determined by which success ratio (successes/total) is larger.
Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern but follow an evolution described by probability distributions. For example, a random sample of individuals from a population refers to a sample where every individual has a known ...
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
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 .