Discrete Random Variable Definition
In probability theory, a discrete random variable is a type of random variable that can take on a finite or countable number of distinct values. These values are often represented by integers or whole numbers, other than this they can also be represented by other discrete values.
For example, the number of heads obtained after flipping a coin three times is a discrete random variable. The possible values of this variable are 0, 1, 2, or 3.
Examples of a Discrete Random Variable
A very basic and fundamental example that comes to mind when talking about discrete random variables is the rolling of an unbiased standard die. An unbiased standard die is a die that has six faces and equal chances of any face coming on top. Considering we perform this experiment, it is pretty clear that there are only six outcomes for our experiment. Thus, our random variable can take any of the following discrete values from 1 to 6. Mathematically the collection of values that a random variable takes is denoted as a set. In this case, let the random variable be X.
Thus, X = {1, 2, 3, 4, 5, 6}
Another popular example of a discrete random variable is the number of heads when tossing of two coins. In this case, the random variable X can take only one of the three choices i.e., 0, 1, and 2.
Other than these examples, there are various other examples of random discrete variables. Some of these are as follows:
- The number of cars that pass through a given intersection in an hour.
- The number of defective items in a shipment of goods.
- The number of people in a household.
- The number of accidents that occur at a given intersection in a week.
- The number of red balls drawn in a sample of 10 balls taken from a jar containing both red and blue balls.
- The number of goals scored in a soccer match.
Discrete Random Variable
Discrete Random Variables are an essential concept in probability theory and statistics. Discrete Random Variables play a crucial role in modelling real-world phenomena, from the number of customers who visit a store each day to the number of defective items in a production line. Understanding discrete random variables is essential for making informed decisions in various fields, such as finance, engineering, and healthcare. In this article, we’ll delve into the fundamentals of discrete random variables, including their definition, probability mass function, expected value, and variance. By the end of this article, you’ll have a solid understanding of discrete random variables and how to use them to make better decisions.