Therefore, the players maximize the mathematical expectation of the cost function.
2.
Such a bettor's mathematical expectation can be expressed as follows:
3.
In the absence of stability violation, the sample mean and the average of mathematical expectations follow to a certain number.
4.
If " X " is a random variable taking values in the domain of, then . ( Here denotes the mathematical expectation .)
5.
The looked for average aggregated estimation of objects quality level may be identified now with mathematical expectation of corresponded random aggregated index Q ( I ).
6.
According to this analysis, the average bettor's mathematical expectation would not provide a profit, but a loss because his expectation is a negative gain every bet.
7.
He did this by reverse engineering a stochastic process for income for which Cagan s expectation formula equals a mathematical expectation of future values conditioned on the infinite history of past incomes.
8.
The formula can be derived by calculating the mathematical expectation of the " amount of information " contained in a digit from the information source . " See also"
9.
Investigations show that in the presence of statistical stability violation the sample mean of the " random sample " tends to the average of mathematical expectations as well as in the absence of statistical stability violation.
10.
Bernoulli assumed that " a poor man generally obtains more utility than a rich man from an equal gain " an approach that is more profound that the simple mathematical expectation of money as it involves a law of " moral expectation ".
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