Random variable or stochastic variable is a value which is calculated from a measurement or manipulation of some random process. Random variable is a function of probability and statistics to maps the events or results (outcomes). It can be defined as possible values to represent the possible outcomes of a performed experiment or test. A Random variable can have different values at a time depending on its probability distribution (which is used to describe the probabilities of different occurring values). In brief, realizations of random variable are defined as random variables. Some good examples of random variables are Boolean values, complex numbers, functions, matrices, manifolds, sequences, sets, shapes and processes.
Random variables are used in the sciences and engineering to make prediction based on available dated acquired by the scientific experiments. These are also a tool to make predictions in games of chance and stochastic events. It is also used to compute Chi-square distribution. We can categorize random variables in three different categories—
Continuous random variables: In continuous random variables, probability of a specific value becomes zero meanwhile the probability of two or more infinite sets of values may be positive.
Mixed random variables: Besides both these types of random variables, a random variable may be mixed having qualities of both variations of its.
All the three types of categorization of random variation are equivalent to the classification of probability distributions.