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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].
More formally, it is the partial derivative of the total expected value with respect to time. Cost of Delay combines an understanding of value with how that value leaks away over time. It is a tactic that helps communicate and prioritize development decisions by calculating the impact of time on value creation & capture. [2]
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
The total dead time of a detection system is usually due to the contributions of the intrinsic dead time of the detector (for example the ion drift time in a gaseous ionization detector), of the analog front end (for example the shaping time of a spectroscopy amplifier) and of the data acquisition (the conversion time of the analog-to-digital converters and the readout and storage times).
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 ).
In epidemiology, the excess deaths or excess mortality is a measure of the increase in the number of deaths during a time period and/or in a certain group, as compared to the expected value or statistical trend during a reference period (typically of five years) or in a reference population.
In statistics, gambler's ruin is the fact that a gambler playing a game with negative expected value will eventually go bankrupt, regardless of their betting system.. The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet ...
The term sound effect dates back to the early days of radio. In its Year Book 1931 the BBC published a major article about "The Use of Sound Effects". It considers sound effects deeply linked with broadcasting and states: "It would be a great mistake to think of them as analogous to punctuation marks and accents in print.