A variable is a symbol that acts on functions, formulas, algorithms, and propositions in mathematics and statistics. Depending on their characteristics, variables are classified differently.
The random (or stochastic) variable is the function that assigns possible events to real numbers (figures), whose values are measured in random experiments. These possible values represent results of experiments not yet performed or uncertain values. It should be noted that randomized experiments are those that, carried out under the same conditions, can offer different results. Flip a coin to see if heads or tails is such an experiment.
The random variable, in short, allows us to give a description of the probability that certain values are adopted. It is not known exactly what value the variable will take 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. In the field of probability and statistics, a probability distribution is known as a function that assigns to each of the events defined in a random variable a value that indicates the probability that the event it represents will occur. To define it, we start from the set of all events, each one being the range of the variable in question. From a formal theoretical perspective, random variables are functions defined on a probability space (also called a probabilistic space), a mathematical concept that models a given random experiment. In general, 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; * the group of all random events. The pair formed by this component and the previous one is called the measurement space; * finally, a probability measure that determines the probability of each event occurring and that serves to verify that Kolmogorov’s axioms are fulfilled. Kolmogorov’s axioms are summarized as follows: 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, the sum of their probabilities is equal to the probability that one of them occurs. Mutually exclusive events or events, on the other hand, are those that cannot occur simultaneously.
Discrete random variables are those whose classification is made up of a finite number of elements or their components can be numbered 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 bound to a path or range that, in theory, covers all real numbers, even if only a certain number of values can be accessed (such as the height of a group of people). This concept also takes advantage of programming, where there is a clear limitation in the range of possible elements, since they depend on memory, which is finite. The greater the space available for the probability distribution and the complexity that the hits can have, the more realistic the simulation will be. One of the areas in which they can be used may be random variable and real-time character animation, where a three-dimensional model is intended to react and interact with the environment realistically while being controlled by a human. being.
