A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which...

there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence in distribution...

many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with...

mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p {\displaystyle p} and the...

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

complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take...

In statistics, the algebra of random variables provides rules for the symbolic manipulation of random variables, while avoiding delving too deeply into...

real-valued random variables, each of which clusters around a mean value. The multivariate normal distribution of a k-dimensional random vector X = (...

probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either...

parameter. The distribution is supported on the interval [0, ∞). If a random variable X has this distribution, we write X ~ Exp(λ). The exponential distribution...

could be well modeled by a Poisson distribution.: 23-25 . A discrete random variable X is said to have a Poisson distribution with parameter λ > 0 {\displaystyle...

is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the...

parameterization, both offering insights into the behavior of gamma-distributed random variables. The gamma distribution is integral to modeling a range of phenomena...

a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events...

distributed random variable defined over N {\displaystyle \mathbb {N} } , and Y {\displaystyle Y} is a geometrically distributed random variable defined over...

In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely...

is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f ( x ) =...

continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then...

a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables in a probability space, where the...

Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is...

broader parameter space Transforms (function of a random variable); Combinations (function of several variables); Approximation (limit) relationships; Compound...

distribution remains a good approximation, and is widely used. If the random variable X follows the binomial distribution with parameters n ∈ N {\displaystyle...

modern practice of random forests, in particular: Using out-of-bag error as an estimate of the generalization error. Measuring variable importance through...

the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability...

random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable...

theory, a subgaussian distribution, the distribution of a subgaussian random variable, is a probability distribution with strong tail decay. More specifically...

probability distribution of a mixed random variable consists of both discrete and continuous components. A mixed random variable does not have a cumulative distribution...

distribution of the ratio of two independent normally distributed random variables with mean zero. The Cauchy distribution is often used in statistics...

continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable)...

of the squares of k {\displaystyle k} independent standard normal random variables. The chi-squared distribution χ k 2 {\displaystyle \chi _{k}^{2}} is...