Random Variable

Reviewed by Sweta | Updated on Jul 26, 2021



Random variable refers to a variable whose value is not known or a function which obtains its values from the outcome of a random experiment. Random variables are assigned different letters and may be discrete or continuous. The variables are real numbers which may either have specific values or may assume any values in a continuous range.

Understanding Random Variable

Random variables are part of random experiments conducted in probability and statistics. Random experiments are carried to quantify the values of random variables.

For example, in a random experiment of a selection of one ball each from two packs containing numbered balls from 1 to 20. Suppose the letter X is designated to represent the sum of the numbers, the random value of X could be 2 (1+1), 40 (20+20), or somewhere between 1 and 20, ranging from the highest number 1 to the lowest numbered ball 20.

The value of a random variable is not calculated like an algebraic variable. In an algebraic equation, the value of the unknown variable can be calculated. For example, in an equation 15+x=20, we can calculate the value of the variable as 5. But, unlike an algebraic variable, a random variable may assume any value from a set of values.

In practical scenarios, random variables are assigned to risk models to determine the probability of occurrence of an adverse event. For example, random values may be assigned to determine the return of investment for a company after a certain number of years. Random experiments are done using tools, such as sensitivity analysis tables, to obtain values for decision making.

A random experiment with random variables is generally probability distribution where any of the values have an equal chance of occurrence.


Random variables are used in all types of economic and financial decision making to carry out random experiments. Statistical tools and probability distribution are used to determine the probable outcomes in a given scenario, and thus facilitate decision making.

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