# Expected Value

Expected value refers to an interesting techniques that is often used in machine learning theory, statistics, probability analysis or during general big data analysis. The idea is to use a probability in order to tell what outcomes can be expected in the long run. **To calculate an expected value one simply multiplies each outcome by its given probability and add all those results together to one value.** In other words it is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then adding all of those values to one key value. Expectation, the mean or the first moment are all terms also used instead of expected value itself.

There are a wide variety of applications and in order to provide one example application domain we can refer to investments. By using the expected value an investor can choose the scenario most likely to give them their desired investment outcome. Another often application domain quoted is a board game with the probabilities that determine how many spaces a board game player will move forward on each turn. **If we assume the following probabilities for a player of the board game that are 0.5 of moving 1 space, 0.25 of moving 2 spaces, and 0.25 of moving 3 spaces, then we can say that the expected value is 1.75.** The reasoning behind this value is that 0.5 * 1 + 0.25 * 2 + 0.25 * 3 equals to 1.75. Hence the calculation of the expected value is quite simple if the related probabilities are known.

## Details on Expected Value

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