Continuous random variables have many applications. Baseball batting averages, IQ scores, the length of time a long distance telephone call lasts, the amount of money a person carries, the length of time a computer chip lasts, rates of return from an investment, and SAT scores are just a few. The field of reliability depends on a variety of continuous random variables, as do all areas of risk analysis.
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.