Difference Between Variable and Random Variable

Variable vs Random Variable

Generally the concept variable can be defined as a quantity which can assume different values. Any theory based on mathematical logic requires some sort of symbols for the representation of the concerned entities. These variables have different properties based on the way they are defined.

More about Variable

In the mathematical context, a variable is a quantity which has a changing or a variable magnitude. Commonly (in algebra) it is represented by an English letter or a Greek letter in the lower case. It is common practice to call this symbolic letter the variable.

Variables are used in equations, identities, functions, and even in geometry. Few of the use of variables are as follows. Variables can be used to represent unknowns in equations such as x2-2x+4=0. It also can represent a rule between two unknown quantities like y=f(x)=x3+4x+9.

In mathematics, it is customary to emphasize the valid values for the variable, which is called the range. These limitations are deduced from the general properties of the equation or by definition.

Variables are also categorized based on their behaviour. If the variable’s changes are not based on other factors, it is called an independent variable. If the variable’s changes are based on some other variable(s), then it is known as a dependent variable. The term variable is used in the field of computing also, especially in programming. It refers to a block memory in the program where different values can be stored.

More about Random Variable

In probability and statistics, a random variable is that subjected to the randomness of the entity described by the variable. And the random variables are mostly represented by letters in upper case. A random variable can assume a value related to a state, such as P(X=t), where t represent a specific event in the sample. Or It can represent a series of events or possibilities such as E(X), where E represents a dataset, which is the domain of the random variable.

Based on the domain, we can categorize variables into discrete random variables and continuous random variables. Also, in statistics, independent and dependent variables are termed as Explanatory variable and Response variable respectively.

The algebraic operations performed on random variables are not the same as for algebraic variables. For example, addition of two random variables may have a different meaning than the addition of two algebraic variables. For example, an algebraic variable gives x + x = 2x , but + X ≠ 2X (this depends on what the random variable actually is).

Variable vs Random Variable

• A variable is an unknown quantity that has an undetermined magnitude, and random variables are used to represent events in a sample space or related values as a dataset. A random variable itself is a function.

• A variable can be defined with domain as a set of real numbers or complex numbers while random variables can be either real numbers or some discrete non mathematical entities in a set. (A random variable can be used to denote an event related to some object, actually the purpose of a random variable is to introduce a mathematically manipulative value to that event)

• Random variables are associated with probability and probability density function.

• Algebraic operations performed on algebraic variables may not be valid for random variables.