Random Variables
Understanding random variables
Idea of this post is to understand what are random variables, why they are required and how these random variables are different than the variables that we use in algebra classes.
What are random variables?
Random variables are ways to map outcomes of random processes (also refereed as experiments) to numbers. Let’s dive deep into this definition to understand completely.
We can list various random processes (or experiments) such as flipping a coin, rolling a dice, measuring the rain that might fall tomorrow etc.. but in order to understand random variable, let’s pick up one particular process such as flipping a coin. In order to quantify the outcomes of a coin flip, let’s use a variable X such that:
- X = 0 if the flip of the coin is a head.
- X = 1 if the flip of the coin is a tail.
We used variable X to represent the outcome of a coin flip. Such variables are called Random Variables.
Why random variables are required?
It will become more clear as we get little bit deeper into probability but the simple interpretation would be as soon as we quantify the outcomes, it becomes easy to do little bit more math on these outcomes and you can start to use more mathematical notations. For example: It would be easy to write p(x=H) instead of p(outcome of coin flip equals to head).
How Random Variables are different than traditional variables that we use in algebra?
We might have seen some equations in algebra classes such as x+8=9 [1], y=x+4 [2] etc.. The intuition behind this section is to understand how these x and y are different than X that we came across earlier.
In equation[1], you can solve for x and in equation [2] you can see how y varies as x changes. That’s not going to be the case with a random variable. A random variable can take many different values with different probabilities unlike x and y in equation[1] and [2].
Find next post Types Of Random Variables
