Continuous random variables are variables that can take any value within a certain range or interval. They are often used in probability and statistics to model real-world phenomena, such as the height of a person, the weight of an object, or the time it takes to complete a task.

Unlike discrete random variables, which can only take on a finite or countable number of values, continuous random variables can take on an infinite number of values. For example, the height of a person can be any value between 0 and infinity, and the weight of an object can be any value between 0 and infinity as well.

The probability distribution of a continuous random variable is described by a probability density function (PDF), which gives the probability of the variable taking on a certain value within a certain interval. The area under the PDF curve between two values represents the probability of the variable taking on a value within that interval.

The cumulative distribution function (CDF) of a continuous random variable gives the probability that the variable takes on a value less than or equal to a certain value. The CDF is the integral of the PDF from negative infinity to the given value.

Some common examples of continuous random variables include:

- The height of a person
- The weight of an object
- The time it takes to complete a task
- The distance traveled by a car
- The temperature of a room
- The amount of rainfall in a certain area.