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...

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

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...

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

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...

calculation of the sum of normally distributed random variables is an instance of the arithmetic of random variables. This is not to be confused with the sum...

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...

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

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

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...

for every trial. If these conditions are true, then the geometric random variable Y is the count of the number of failures before the first success....

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

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)...

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

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

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...

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...

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...

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

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

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

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

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

population (sampling without replacement from a finite population). A random variable X {\displaystyle X} follows the hypergeometric distribution if its...

This distribution satisfies the definition of "random variable" even though it does not appear random in the everyday sense of the word; hence it is considered...

theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. Thus...

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

of the squares of k {\displaystyle k} independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution...