ABSTRACT

If you ´ip a coin 10 times, you expect to get 5 heads. If you ´ip a coin 1000 times, you expect to get 500 heads. If you invest 100,000 in a stock that has had a consistent 5% annual return, you expect to earn 5,000 after a year. But you won’t necessarily get 5 heads in 10 ´ips, it is very unlikely that you will get 500 heads out of 1000 ´ips, and it is extremely unlikely that your earnings will be precisely 5000 on the investment. Expected value, therefore, is not actual observed data; rather, it is kind of an average. An observed statistic may be higher than its expected value or it may be lower. Rarely-if ever-is the observed value equal to the expected value. Yet the expected value is useful for making decisions everywhere, no matter whether you are interested in how to invest your money, how to design an automobile tire, how to treat a hospital patient, or how many hunting licenses to issue. In this chapter, we clarify what precisely is meant by expected value and provide applications.