July 10, 2020

Variability is widely used in the business world. As a matter of fact, many industries rely on variability. When we talk about variability, there are many possibilities so it becomes necessary for us to model it with the help of random variables. So, the question is, what is a random variable? The basic definition (that you will find in many textbooks) is that a **random variable** is a numerically valued variable (or you can say a numerical description) that has different values for different outcomes of a statistical experiment.

To make it simpler to understand, we inherit an example of the landing of a space shuttle. The objective of this experiment is to find the right height for opening the parachute for a successful landing. So, the experts took some random variables (for instance, 3m, 5m, 7m, 10m, etc.) and then they performed a simulation against it to find the perfect height for a successful landing of the space shuttle. For each value of height, the results were recorded, and then the results were interpreted by a statistician. Let’s say that neither of the values of height provided good results so what is next? Take another set of data and then reperform the simulation? This can take days for finding the right value! This is where different formulas for random variables to get the closest answer but that is a very huge debate and let’s stick to random variables for now.

After reading the above example, you will have an idea of how the concept of a random variable is used in the business world. However, we have some other applications where random variable plays an important role. Below are some applications of a random variable:

- The return on an investment
- The cost of an equity
- Number of visitors visiting your store or website
- Sales volume of products on a particular day
- The turnover rate for an organization

## Types of Random Variable

Remember we talked about different formulas? There are many formulas and each one of them has a condition. If the conditions don’t fulfill then we don't use that formula, instead, we search for the right formula to get an accurate result. As mentioned above, many industries rely on random variables so just a small mistake can spell a disaster for that industry. There is absolutely no chance for error. Picking up the right formula is a difficult job since you need to memorize conditions. However, statisticians have made this easier by categorizing them. Today, there are two types of random variables:

### Discrete Random Variable

The best way to describe a **discrete random variable** is that can take a countable number of possibilities. In simple words, a discrete random variable works with an integer value only.

For example,

The number of children in a family: 2,3,4 …

The score obtained by throwing a dice: 1,2,3,4…,6

The sum of scores of two dices: 2,3,4…,12

Total number of cellphones sold: 0,1,2,3…

Total number of visitors: 0,1,2,3…

Furthermore, a discrete random variable deals with a finite or an infinite series of values.

### Continuous Random Variable

In simple words, a **continuous random variable** can take all possible values within an interval. In other words, it works with an uncountable number of possibilities. For example

The height of students in a class: 5ft-4in, 6ft-1in, 5ft-7in …

The hours of duration of a battery: 15h, 24h, 54h, 10h …

The interest rate: 1.25%, 4.3%, 2.1%, 6.375%

The price of a stock: any positive values

## Point to be Noted

Always remember, if you are dealing with integer or rational numbers then you need to use the discrete random variable concept. However, if the numbers are real numbers then you need to use the continuous random variable concept.