theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random variable has the...

to the use of independent and identically distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases...

theorem (CLT) states that, in many situations, when independent and identically distributed random variables are added, their properly normalized sum tends...

real-valued, independent and identically distributed random variables and let N ≥ 0 be an integer-valued random variable that is independent of the sequence...

{\displaystyle X,Y} are independent The Erlang distribution is the distribution of the sum of k independent and identically distributed random variables, each having...

be derived from the variance of a sum of independent random variables, given the definition of variance and some properties thereof. If x 1 , x 2 , …...

(statistics) Independent and identically distributed random variables Mean dependence Normally distributed and uncorrelated does not imply independent Russell...

samples be independent and have identical probability distribution (in other words independent and identically distributed random variables are the simplest...

X_{1},X_{2},\ldots ,X_{n}} be n {\displaystyle n} independent and identically distributed random variables following an exponential distribution with rate...

\ldots ,X_{n}} are independent and identically distributed random variables with the same arbitrary distribution, zero mean, and variance σ 2 {\textstyle...

Peter J. (2016). "Entropy of the sum of two independent, non-identically-distributed exponential random variables". arXiv:1609.02911 [cs.IT]. Ibe, Oliver...

statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is...

of checking equality of certain functions of independent, identically distributed (IID) random variables. However, the moment generating function exists...

a breathalyzer connected to a vehicle's engine Independent and identically distributed random variables in probability theory Interaural intensity difference...

{1}{n}}{\sum _{k=1}^{n}X_{k}}} of a sequence of independent and identically distributed random variables X k {\displaystyle X_{k}} converges towards their...

of properly normalized maxima of a sequence of independent and identically distributed random variables. that a limit distribution needs to exist, which...

number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable. The result...

(1)} That is: given a sequence of independent and identically distributed random variables, each having mean zero and positive variance, if additionally...

characterized by the steps being defined by independent and identically distributed random variables. Random walks can take place on a variety of spaces...

exist n {\displaystyle n} independent identically distributed random variables whose sum is also geometrically distributed. This is because the negative...

Kirkwood approximation Independent identically-distributed random variables Independent and identically-distributed random variables Statistical independence...

the sequence of inter-arrival times are independent and identically distributed exponential random variables having mean 1/λ.: 317–319  The cumulative...

Binomial distributed random variables X ~ B(n, p) and Y ~ B(m, p) is equivalent to the sum of n + m Bernoulli distributed random variables, which means...

1\,\}} are independent and identically distributed random variables, with distribution function G, which are also independent of { N ( t ) : t ≥ 0 } . {\displaystyle...

density, ƒn is its estimate based on a sample of n independent and identically distributed random variables. Here, E denotes the expected value with respect...

any sequence of random n × n matrices whose entries are independent and identically distributed random variables, all with mean zero and variance equal...

identically distributed (i.i.d.) random variables on [0,1]. Then let Xi = a+(b - a)Ui for i= 1, 2, ..., n. Then X1, X2, ..., Xn are independent and identically...

distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has...

of independent, identically distributed random variables is a mixing random process in discrete time; "mixing" means, roughly, that random variables temporally...

Still more general are decomposable processes. Independent and identically distributed random variables Wiener process Poisson process Gamma process Markov...