What Is Expectation Value?

In probability theory and statistics, the expected value (or mathematical expectation or mean value , also referred to as expectation , which is referred to as physics in the short term) refers to the probability of each possible outcome in a discrete random variable test multiplied by its result sum. ^[1]

The expected value is the average value of the equivalent "expectation" calculated from the results of a randomized trial repeated at the same opportunity multiple times. It should be noted that the expected value is not necessarily equal to the "expectation" in common sense-the "expected value" may not be equal to every result. (In other words, the expected value is the average of the variable's output values. The expected value is not necessarily included in the variable's output value set.)

Expected value

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In statistics, when estimating the expected value of a variable, a frequently used method is to repeatedly measure the value of this variable, and then use the average value of the obtained data as an estimate of the expected value of this variable.

In probability distributions, expectation and variance or standard deviation are important characteristics of a distribution.

In classical mechanics, the algorithm of the center of gravity of the object is very similar to the algorithm of the expected value.

The expected value can also be calculated by the variance calculation formula