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Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would "expect" to get in reality.
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
The "explained" component ( [|]) is the variance of the expected values, i.e., it represents the part of the variance that is explained by the variation of the average value of for each group. Weight of dogs by breed
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
where is the expected value. That is, = =. (When such a discrete weighted variance is specified by weights whose sum is not 1, then one divides by the sum of the weights.) The variance of a collection of equally likely values can be written as
In decision theory, the expected value of sample information (EVSI) is the expected increase in utility that a decision-maker could obtain from gaining access to a sample of additional observations before making a decision.
Second, it is also used to abbreviate "expect value", which is the expected number of times that one expects to obtain a test statistic at least as extreme as the one that was actually observed if one assumes that the null hypothesis is true. [49] This expect-value is the product of the number of tests and the p-value.
The moment generating function of a real random variable is the expected value of , as a function of the real parameter . For a normal distribution with density f {\textstyle f} , mean μ {\textstyle \mu } and variance σ 2 {\textstyle \sigma ^{2}} , the moment generating function exists and is equal to