RANDOM VARIABLE

A variable is a symbol that acts on functions, formulas, algorithms, and propositions in mathematics and statistics. According to their characteristics, the variables are classified differently.

Random variable

The random (or stochastic ) variable is the function that assigns possible events to real numbers (figures), whose values ​​are measured in randomized experiments . These possible values ​​represent the results of experiments that have not yet been carried out or uncertain amounts.

It should be noted that randomized experiments are those that, developed under the same conditions, can offer different results . Throw a coin into the air to see if it comes up heads or tails is an experiment of this kind .

The random variable, in short, allows us to offer a description of the probability that certain values are adopted . It is not known precisely what value the variable will adopt when it is determined or measured, but it is possible to know how the probabilities associated with the possible values ​​are distributed. Chance affects this distribution .

It is known as probability distribution , within the scope of probability and statistics, to a function that gives each of the events that are defined on a random variable a value that denotes how likely it is that the event it represents will take place . To define it, we start from the set of all events, each one of them being the range of the variable in question.

From a formal theoretical perspective, random variables are functions that are defined on a probability space (also called probabilistic space ), a concept in mathematics that models a certain random experiment. Typically, a probability space has the following three components:

* first, a set called the sample space , which brings together all the possible results of the experiment, which are known as elementary events ;

Random variable* the group of all random events. The pair made up of this component and the previous one is called the measurement space ;

* finally, a probability measure that determines the probability that each event takes place and that serves to verify that Kolmogórov's axioms are fulfilled .

Kolmogórov's axioms are summarized below: the certainty that the sample space is present in the random experiment; To determine the probability of an event, a number between 0 and 1 is assigned; If we are faced with mutually exclusive events, then the sum of their probabilities is equal to the probability that one of them occurs. The mutually exclusive events or events, on the other hand, are those that cannot take place in a contemporary way.

The discrete random variables are those whose rank is formed by a finite number of elements or their components may be listed sequentially. Suppose a person rolls a die three times: the results are discrete random variables, since values ​​from 1 to 6 can be obtained .

Instead, the continuous random variable is linked to a path or range that covers, in theory , all of the real numbers, even if only a certain number of values ​​are accessible (such as the height of a group of people).

This concept is also used in programming, where there is a clear limitation for the range of possible elements, since this depends on memory, which is finite. The larger the space available for the probability distribution and the complexity of the events, the more realistic the simulation will be. One of the areas in which the random variable can be useful is real-time character animation, where a three-dimensional model is intended to react and relate to the environment in a realistic way while being controlled by a human being.

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