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Randomness of the Random variable

Let’s start exploring the topic with an instance. Suppose you are the shopkeeper, many people enter the shop each day during the month. Not everyone makes a purchase each day. Someday, few units are sold. The next day, no sell has made. On the third day, many have been to the shop and many people made a purchase from the shop and so on.


So, what can be deduced from above is that the number of people making purchase is random. We cannot answer a specific value rather it gives range of answers as one day 4 customers make a purchase while another day 18 and the next day even zero sales can be made.


Now, we are in position to define the random variable and understand why it is called Random variable?

While conducting any statistical experiment we get sort of outcomes that are random in nature. Due to their randomness, we assign a single variable (Say X) to various random outputs, hence, called Random Variable. Thus, a Random variable is the presentation of the various numerical outcomes. From the above example, the random variable is the number of people making purchases or the number of people entering the shop.

It can be represented as:-

X: Number of people making purchase each day during month OR

X: 0, 1, 2, 3 ….18

Clearly, our work is reduced by assigning a random variable X. Writing just p(X= 2) is enough which similarly means the probability of exactly two people make a purchase during a day.

Note: - Those variables or outcomes can represent anything like the probability of claims, number of claims, and the number of ‘Successes’.




Random variables are Discrete and continuous in nature.


The variable which assumes point values or countable values or distinct value is said to be Discrete (X: 0, 1, 2). Here, X a random variable taking value 0, 1, or 2. For instance, the number of electric vehicles sold monthly during the year is discrete.

The variable which assumes any real value and take infinite many value is said to be Continuous Random Variable (X: [0, 2]). Here, X can take any real value between 0 and 2. For instance, the price of a stock during the day is continuous.

The random variable is very important in the understanding probability distribution.


Lets Check what you have learned so far.


Written by Deepak Agarwal ( pursuing graduation from PGDAV College, University of Delhi and has cleared 4 actuarial papers from IFOA )

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