The values of discrete and continuous random variables can be ambiguous. For example, if $$X$$ is equal to the number of miles (to the nearest mile) you drive to work, then $$X$$ is a discrete random variable. You count the miles. If $$X$$ is the distance you drive to work, then you measure values of $$X$$ and $$X$$ is a continuous random variable. For a second example, if $$X$$ is equal to the number of books in a backpack, then $$X$$ is a discrete random variable. If $$X$$ is the weight of a book, then $$X$$ is a continuous random variable because weights are measured. How the random variable is defined is very important.