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Discrete random variables are variables that take distinct or separate values, such as integers or countable categories. Continuous random variables, on the other hand, are variables that take an infinite number of values within an interval, such as any real number within a range. For example, the number of students in a classroom is a discrete variable, while the height of a person is a continuous variable.

A continuous random variable might be preferred in a scenario where precision is crucial and the number of pages in a book should be considered as a continuous quantity instead of an integer count. Consider the following scenario: A researcher is studying the relationship between the thickness of a book and its number of pages. The thickness of the book may vary due to factors such as the paper's thickness, the cover's thickness, and the binding. It is essential to get an exact measure of the relationship between all these factors and the number of pages, so a more accurate model would be needed. In this situation, the number of pages could be represented as a continuous random variable rather than a discrete random variable to account for the variations in thickness accurately.