probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability...

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

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

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

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

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 , …...

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

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

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

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

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

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

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

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

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

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

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

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

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

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...

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

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

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

possible data compression for data whose source is an independent identically-distributed random variable, and the operational meaning of the Shannon entropy...

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...

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

stochastic processes, such as random graphs. Suppose that a problem involves independent and identically-distributed random variables and that estimation of a...

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

assumption that the win–loss outcomes of each bet are independent and identically distributed random variables, an assumption which is valid in many realistic...