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Any definition of expected value may be extended to define an expected value of a multidimensional random variable, i.e. a random vector X. It is defined component by component, as E[X] i = E[X i]. Similarly, one may define the expected value of a random matrix X with components X ij by E[X] ij = E[X ij].
Expected value of sample information (EVSI) is a relaxation of the expected value of perfect information (EVPI) metric, which encodes the increase of utility that would be obtained if one were to learn the true underlying state, .
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 ...
Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized and explored by the statistician Sir Ronald Fisher (following some initial results by Francis Ysidro Edgeworth ).
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
Science. Expectation (philosophy) Expected value, in mathematical probability theory; Expectation value (quantum mechanics) Expectation–maximization algorithm, ...
In science, and most specifically chemistry, the accepted value denotes a value of a substance accepted by almost all scientists and the experimental value denotes the value of a substance's properties found in a localized lab.
This proposition is (sometimes) known as the law of the unconscious statistician because of a purported tendency to think of the aforementioned law as the very definition of the expected value of a function g(X) and a random variable X, rather than (more formally) as a consequence of the true definition of expected value. [1]