Pronunciation: [ɛkspˈɛktɪd vˈaljuːz] (IPA) 
Expected values is a term commonly used in statistics, and is pronounced /ɪkˈspɛktɪd ˈvæljuːz/. The first syllable, "ex", is pronounced with the short "i" sound /ɪ/, followed by "spect" pronounced as /spɛkt/. The last syllable, "ed", is pronounced as /ɪd/. The second word, "values", has stress on the first syllable and is pronounced as /ˈvæljuːz/. The "al" in "values" is pronounced as the "ul" sound /uːl/.
Expected values are a statistical concept used in probability theory and decision analysis to estimate the average outcome of a random event. It represents the anticipated or predicted value of a specific event or experiment, calculated by multiplying each possible outcome by its associated probability and summing the results.
In more detail, the expected value is computed by considering all possible outcomes of an event and assigning a probability to each outcome. Each outcome is then multiplied by its corresponding probability, and all these products are summed together. This calculation results in a single value that represents the average or "expected" outcome of the event.
Expected values are particularly valuable in decision-making scenarios involving uncertainty. They allow individuals to assess potential outcomes and make informed choices based on their understanding of the probabilities associated with those outcomes. For example, in gambling or investment decisions, expected values can help individuals determine the probability-weighted average return they may expect from a particular bet or investment.
Expected values can also be used to evaluate the fairness or profitability of different options. If the expected value of an option is positive, it suggests that the choice has a favorable average outcome. Conversely, a negative expected value implies an unfavorable average outcome. By considering expected values, individuals can make rational decisions that maximize their chances of achieving desirable outcomes.
The term "expected value" in statistics comes from the concept of mathematical expectation or expected value, which has its roots in probability theory. The word "expected" refers to the anticipation or prediction of a certain outcome, while "value" signifies the numerical result or outcome itself. The concept of expected value emerged from the works of mathematicians and statisticians in the 17th and 18th centuries, such as Jacob Bernoulli and Pierre-Simon Laplace, who aimed to quantify uncertain events and predict average outcomes. Over time, this concept became a fundamental principle in probability theory and statistical analysis, leading to the common usage of "expected value" as a statistical term.
