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  2. Independent and identically distributed random variables

    en.wikipedia.org/wiki/Independent_and...

    More formally, it is "a sequence of independent, identically distributed (IID) random data points." In other words, the terms random sample and IID are synonymous. In statistics, " random sample " is the typical terminology, but in probability, it is more common to say " IID ."

  3. Renewal theory - Wikipedia

    en.wikipedia.org/wiki/Renewal_theory

    Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite mean. A renewal-reward process additionally has a random sequence of rewards incurred at each holding time, which are IID but need not be independent of the holding times.

  4. Law of large numbers - Wikipedia

    en.wikipedia.org/wiki/Law_of_large_numbers

    Kolmogorov also showed, in 1933, that if the variables are independent and identically distributed, then for the average to converge almost surely on something (this can be considered another statement of the strong law), it is necessary that they have an expected value (and then of course the average will converge almost surely on that). [22]

  5. Exchangeable random variables - Wikipedia

    en.wikipedia.org/wiki/Exchangeable_random_variables

    The property of exchangeability is closely related to the use of independent and identically distributed (i.i.d.) random variables in statistical models. [8] A sequence of random variables that are i.i.d, conditional on some underlying distributional form, is exchangeable.

  6. Stochastic process - Wikipedia

    en.wikipedia.org/wiki/Stochastic_process

    One of the simplest stochastic processes is the Bernoulli process, [80] which is a sequence of independent and identically distributed (iid) random variables, where each random variable takes either the value one or zero, say one with probability and zero with probability .

  7. Hewitt–Savage zero–one law - Wikipedia

    en.wikipedia.org/wiki/Hewitt–Savage_zero–one_law

    Let {} = be a sequence of independent and identically-distributed random variables taking values in a set .The Hewitt-Savage zero–one law says that any event whose occurrence or non-occurrence is determined by the values of these random variables and whose occurrence or non-occurrence is unchanged by finite permutations of the indices, has probability either 0 or 1 (a "finite" permutation is ...

  8. Irwin–Hall distribution - Wikipedia

    en.wikipedia.org/wiki/Irwin–Hall_distribution

    In probability and statistics, the Irwin–Hall distribution, named after Joseph Oscar Irwin and Philip Hall, is a probability distribution for a random variable defined as the sum of a number of independent random variables, each having a uniform distribution. [1] For this reason it is also known as the uniform sum distribution.

  9. Asymptotic theory (statistics) - Wikipedia

    en.wikipedia.org/wiki/Asymptotic_theory_(statistics)

    The law states that for a sequence of independent and identically distributed (IID) random variables X 1, X 2, ..., if one value is drawn from each random variable and the average of the first n values is computed as X n, then the X n converge in probability to the population mean E[X i] as n → ∞. [2] In asymptotic theory, the standard ...