But what is a Random Variable?

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Introduction

Often simple concepts become difficult to grasp because of the terminology and the context in which they are applied. Random Variable was one such confusing (even though simple in the hindsight) aspect for me.

For a software engineer, a variable is of two types — local or global. Often there is a range and bound on the variables when you are writing software but if you add the adjective Random to them it means that they can have any value (although you can still control the randomness using the notion of a seed).

For a cryptographer, randomness is one of the most important properties for his/her algorithms. He/She strives to generate random numbers that should not repeat at all.

From elementary algebra’s perspective, the notion of variable is straight forward i.e it represents an input of your equation and is written on the right side and also represents an output of your equation that is written on the left side. Random aspect generally does not appear or discussed at that level.

Now if you read its definition on Wikipedia or google — What is Random Variable in Statistics?, you will see a statement like this:

A Random Variable is a function that maps outcomes to real values.

A variable that is actually a function ?

For statisticians, this may be fine but for people from other disciplines such as software engineering, this very statement starts to seriously break down the semantics as it perturbs their understanding of 3 very fundamental things they deal with every day — Variables, Functions and Randomness!

Clearly Random Variables of statistics are different creatures and understanding them is fundamental to many other concepts (Gaussian Processes, Bayesian Statistics etc) that either use them and/or build upon them.