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These inequalities are significant for their nearly complete lack of conditional assumptions. For example, for any random variable with finite expectation, the Chebyshev inequality implies that there is at least a 75% probability of an outcome being within two standard deviations of the expected value. However, in special cases the Markov and ...
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 unconditional expectation of rainfall for an unspecified day is the average of the rainfall amounts for those 3652 days. The conditional expectation of rainfall for an otherwise unspecified day known to be (conditional on being) in the month of March, is the average of daily rainfall over all 310 days of the ten–year period that fall in ...
Markov's inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a random variable. Markov's inequality can also be used to upper bound the expectation of a non-negative random variable in terms of its distribution function.
The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then ...
For an illustration, consider the example of a dog show (a selected excerpt of Analysis_of_variance#Example). Let the random variable correspond to the dog weight and correspond to the breed. In this situation, it is reasonable to expect that the breed explains a major portion of the variance in weight since there is a big variance in the ...
The expectancy theory of motivation explains the behavioral process of why individuals choose one behavioral option over the other. This theory explains that individuals can be motivated towards goals if they believe that there is a positive correlation between efforts and performance, the outcome of a favorable performance will result in a desirable reward, a reward from a performance will ...
this being the sample analogue of the expected log-likelihood () = [ ()], where this expectation is taken with respect to the true density. Maximum-likelihood estimators have no optimum properties for finite samples, in the sense that (when evaluated on finite samples) other estimators may have greater concentration around the true ...