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For example, if the variance of a random variable is said to be finite, this implies it is a non-negative real number, possibly zero. In some contexts though, for example in "a small but finite amplitude", zero and infinitesimals are meant to be excluded.
A set of random variables, any two of which are independent. parameter Any measured quantity of a statistical population that summarizes or describes an aspect of the population, e.g. a mean or a standard deviation; often a quantity to be estimated based on the corresponding quantity calculated by drawing random samples from the population. Can ...
Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable. [ note 1 ] For example, when throwing two dice , the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as ...
Once the random relations have been chosen, the resulting random group is defined in the standard way for group presentations, namely: is the quotient of the free group with generators ,, …,, by the normal subgroup generated by the relations , …, seen as elements of :
5. In probability and statistics, may specify the probability distribution of a random variable. For example, (,) means that the distribution of the random variable X is standard normal. [2] 6. Notation for proportionality. See also ∝ for a less ambiguous symbol. ≡ 1.
Using the standard formalism of probability theory, let and be two random variables defined on probability spaces (,,) and (,,).Then a coupling of and is a new probability space (,,) over which there are two random variables and such that has the same distribution as while has the same distribution as .
def – define or definition. deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.) del – del, a differential operator. (Also written as.) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform.
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