What Is The Expected Value

If the expected value exists, this procedure estimates the true expected value in an unbiased manner and has the property of minimizing the sum of the squares of the residuals (the sum of the squared differences between the observations and the estimate). Learn how to calculate the expected value of a random variable, which is the long-run average outcome based on its probabilities. See examples for discrete and continuous distributions, and applications in gambling, finance, and decision-making.

Expected value, in general, the value that is most likely the result of the next repeated trial of a statistical experiment. The probability of all possible outcomes is factored into the calculations for expected value in order to determine the expected outcome in a random trial of an experiment. Definition (informal) The expected value of a random variable is the weighted average of the values that can take on, where each possible value is weighted by its respective probability.

In probability theory, an expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment. Expected value is a measure of central tendency; a value for which the results will tend to. As we noted, the expected value of an experiment is the mean of the values we would observe if we repeated the experiment a large number of times.

(This interpretation is due to an important theorem in the theory of probability called the Law of Large Numbers.) Expected value (EV) is the average value of a random variable, calculated by multiplying each possible outcome by its probability and adding the results. It represents the average outcome expected from a random experiment over many trials.

Expected value is the anticipated value for an investment at some point in the future and is an important concept for investors seeking to balance risk with reward. In probability theory, the expected value (often denoted as $E [X]$ for a random variable $X$) represents the average or mean value of a random experiment if it were repeated many times. The expected value of a random variable depends only on the probability distribution of the random variable.

The expected value has properties that can be exploited to find the expected value of some complicated random variables in terms of simpler ones. These properties allow us to find the expected value of the sample sum and sample mean of random draws with and without replacement from a ...