Difference Between Discrete Random Variable And Continuous Random Variable
The key differences between discrete and continuous random variables are as follows:
| Discrete Random Variable | Continuous Random Variable | |
|---|---|---|
| Definition | Takes on a finite or countably infinite set of possible values. | Takes on any value within a range or interval i.e., can be uncountably infinite as well. |
| Probability Distribution | Described by a probability mass function (PMF), which gives the probability of each possible value. | Described by a probability density function (PDF), which gives the probability density at each possible value. |
| Example | Number of heads in three coin tosses. | Height of a person selected at random. |
| Probability of a single value | Non-zero probability at each possible value. | Zero probability at each possible value. |
| Cumulative Distribution Function | Describes the probability of getting a value less than or equal to a particular value. | Describes the probability of getting a value less than or equal to a particular value. |
| Mean and Variance | Mean and variance can be calculated directly from the PMF. | Mean and variance can be calculated using the PDF and integration. |
| Probability of an Interval | The probability of an interval is the sum of the probabilities of each value in the interval. | The probability of an interval is the area under the PDF over the interval. |
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.