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The expected profit from such a bet will be [$] = $ + $ = $. That is, the expected value to be won from a $1 bet is −$ 1 / 19 . Thus, in 190 bets, the net loss will probably be about $10.
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. [ 1 ]
The theory of median-unbiased estimators was revived by George W. Brown in 1947: [8]. An estimate of a one-dimensional parameter θ will be said to be median-unbiased, if, for fixed θ, the median of the distribution of the estimate is at the value θ; i.e., the estimate underestimates just as often as it overestimates.
In Lindsay and Li's case, the expected information matrix still requires evaluation at the obtained ML estimates, introducing randomness. However, when the construction of confidence intervals is of primary focus, there are reported findings that the expected information outperforms the observed counterpart.
In statistics, expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance (ANOVA). They can be used for ascertaining which statistic should appear in the denominator in an F-test for testing a null hypothesis that a particular effect is absent.
If a vector of predictions is generated from a sample of data points on all variables, and is the vector of observed values of the variable being predicted, with ^ being the predicted values (e.g. as from a least-squares fit), then the within-sample MSE of the predictor is computed as
The expected utility hypothesis imposes limitations on the utility function and makes utility cardinal (though still not comparable across individuals). Although the expected utility hypothesis is standard in economic modelling, it has been found to be violated in psychological experiments.
When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows.