A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables? i. The amount of rain, in inches, that will fall next Friday in Dallas, TX. ii. The major of a randomly drawn student from Arizona State University. iii. The number of books purchased next year by your local library. i only Oii only iii only i and iii and iii i, ii, and iii

The amount of rain in inches that will fall next Friday in Dallas is definitely a random variable because it's based on uncertain weather conditions. Similarly, the number of books purchased next year by your local library is also a random variable, as it depends on future decisions and trends, making it uncertain. However, the major of a randomly drawn student is not a numerical outcome but a categorical one, so it's not a random variable. Therefore, the correct answer is i and iii only! If you're looking to dive deeper, random variables come in two flavors: discrete and continuous. A discrete random variable has specific, separate values—like the number of books—while a continuous random variable can take on any value within a range, such as inches of rainfall. This distinction is crucial for understanding probability distributions! For practical applications, think about how random variables are used in insurance! Actuaries analyze random variables to predict the likelihood of events such as accidents or illnesses. These predictions help companies determine premiums and manage risk effectively. It's fascinating how probability and statistics influence real-world decisions!