Significance of Random Variables

In the context of Data Mining and Analysis

So what is a random variable?

Whenever we study an object, we observe that there are several features that represent that object. These features are called variables. A variable is a placeholder that can store any value, be it an integer, a float, a character or a string. Consider working with a large number of objects. We would find that a single feature can have different values for different objects. For example, say we are analysing the BMI(Body Mass Index) of all male individuals below the age of 20 living in some particular area. On measuring the heights of the individuals we find that values for the height feature are different. This suggests that the values of the variable are subject to some random variation. If this randomness due to chance is significant, then the variable is referred to as a random variable. As a result, a random variable can take on a variety of different values, each with an associated probability equal to the relative frequencies of these different values that it can take. Hence,

Types of Random Variables

From the above definition of random variables, we can make out that a random variable can be of many different types depending upon the attribute of the object being studied.

Different Types of Random Variables
  • Discrete Random Variables- These can take only a countable number of distinct values. For example, the number of rooms in your house or the score you earned in your last exam.
  • Continuous Random Variables- These can take an infinite number of possible values and are usually used in measurements. For example, your weight and height. You might be thinking that a feature like weight can only take countable number of distinct values like 68Kg or 70Kg but if you use a more accurate weighing balance, a value of 68.1Kg could be measured and with an even more accurate weighing balance, a value of 68.13Kg could be measured. What I mean to say is that with the increase in accuracy, infinite number of outcomes are possible. Hence, a continuous random variable is not defined at specific values but over an interval of values.
  • Nominal Random Variables- These can have two or more categories without any intrinsic ordering among them. For example, eye colour can have the values red, green, blue etc.
  • Ordinal Random Variables- It is similar to nominal random variable with an addition of having some ordering or ranking among the categories. For example, Officer ranks can have the values Major, Captain, Lieutenant or Officer Cadet, where there is a specific ordering among them.

Probability Distribution

Now that we are clear with the definition and types of random variables, lets go a little deeper. We know that a random variable can take on different values, each with some associated probabilities. Therefore, a random variable describes the probability of getting that value. If we plot these values against their associated probability, we come up with a probability distribution graph. A probability distribution describes how a random variable is distributed. It shows us which values are most likely to be taken by a random variable and which are less probable.

Importance of Random Variables

Random variables help in determining the probability of an outcome. These have many applications in real life especially in data analysis and decision making. Consider an example where an insurance company provides three different types of health coverage to its customers, these being basic, premium and exclusive. The company provides the insurance plans depending upon various customer features like age, marriage status, salary, BMI, etc. Now assume a young engineer wants to buy insurance, then what kind of plan should be provided to him. After analysing all the customer features the company comes up with the following probability:

  • Basic: 0.62
  • Premium: 0.20
  • Exclusive: 0.18



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