what is expected value 
expected value ev is a term used by those in the investment industry to denote the anticipated average value of an investment at some point in the future investors use expected value to estimate the worth of investments often relative to their risk by calculating evs investors can choose the scenario most likely to produce the outcome they seek in statistics and probability analysis the ev is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values understanding expected valueexpected value refers to the anticipated value of an asset in the future the ev of a random variable gives a measure of the center of the distribution of the variable the ev is essentially the long term average value of the variable because of the law of large numbers the average value of the variable converges to the ev as the number of repetitions approaches infinity ev is also known as expectation the mean or the first moment ev can be calculated for single discrete variables single continuous variables multiple discrete variables and multiple continuous variables for continuous variable situations integrals must be used scenario analysis is one technique for calculating the ev of an investment opportunity it uses estimated probabilities with multivariate models to examine possible outcomes for a proposed investment scenario analysis also helps investors determine whether they are taking on an appropriate level of risk given the likely outcome of the investment the difference between expected value and arithmetic mean is that the first involves a distribution of probability and the second involves a distribution of occurrence formula for expected valuethe formula for expected value is e v p x i x i begin aligned ev sum p x i times x i end aligned ev p xi xi 