A random variable that can assume an infinite number of values is called a continuous random variable.
Continuous random variables are those that can take on any value within a given range or interval. This means that the values are not restricted to discrete numbers, but can include all sorts of fractions and decimals. For example, the height of individuals, the amount of rainfall in a day, or the time it takes to run a marathon can all be modeled as continuous random variables.
The concept of continuous random variables is fundamental in statistics and probability theory, as it helps in understanding phenomena that exhibit variability and allows for the use of calculus to compute probabilities, expected values, and other statistical measures.