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When the image (or range) of is finitely or infinitely countable, the random variable is called a discrete random variable [5]: 399 and its distribution is a discrete probability distribution, i.e. can be described by a probability mass function that assigns a probability to each value in the image of .
Random variable: takes values from a sample space; probabilities describe which values and set of values are taken more likely. Event : set of possible values (outcomes) of a random variable that occurs with a certain probability.
random variable A measurable function on a probability space, often real-valued. The distribution function of a random variable gives the probability of the different values of the variable. The mean and variance of a random variable can also be derived. See also discrete random variable and continuous random variable. randomized block design range
These correspond to aggregates of random variables described using graphical models, where individual random variables are linked in a graph structure with conditional distributions relating variables to nearby variables. Multilevel models are subclasses of Bayes networks that can be thought of as having multiple levels of linear regression.
A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness .
A more general case of this concerns the distribution of the product of a random variable having a beta distribution with a random variable having a gamma distribution: for some cases where the parameters of the two component distributions are related in a certain way, the result is again a gamma distribution but with a changed shape parameter ...
the product of two random variables is a random variable; addition and multiplication of random variables are both commutative; and; there is a notion of conjugation of random variables, satisfying (XY) * = Y * X * and X ** = X for all random variables X,Y and coinciding with complex conjugation if X is a constant.