A discrete random variable is a variable that can only take on a finite or countably infinite number of values. It is often used in probability theory to model situations where the outcome can only be one of a finite number of possibilities.

Examples of discrete random variables include:

- The number of heads obtained in a series of coin tosses
- The number of cars passing through a toll booth in an hour
- The number of students in a classroom who have a birthday in a particular month
- The number of defective items in a production run

Discrete random variables can be described using a probability distribution, which assigns a probability to each possible value of the variable. The probability distribution can be represented using a probability mass function (PMF), which gives the probability of each possible value of the variable.

The mean, or expected value, of a discrete random variable can be calculated by multiplying each possible value by its probability and summing the results. The variance and standard deviation of a discrete random variable can also be calculated using a similar formula.

Overall, discrete random variables are an important tool in probability theory and can be used to model a wide range of real-world situations.