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The latter proposition may remain valid, even if it is certain that some instances of the generalisation are false. It is more likely than not, for example, that any number will be divisible either by two or by three, but it is not more likely than not that all numbers are divisible either by two or by three.
Immigration and Naturalization Service v. Predrag Stevic, 467 U.S. 407 (1984), was a Supreme Court of the United States decision that held if an alien seeks to avoid deportation proceedings by claiming that he will be persecuted if he is returned to his native land, he must show a "clear probability" that he will be persecuted there.
The heart of the standard articulated by the BIA was its "empirical conclusion, based on its experience in adjudicating asylum applications, that if the facts establish such a basis for an alien's fear, it rarely will make a difference whether the judge asks if persecution is 'likely' to occur or 'more likely than not' to occur.
[1] [2] It should not be confused with risk aversion, which describes the rational behavior of valuing an uncertain outcome at less than its expected value. When defined in terms of the pseudo-utility function as in cumulative prospect theory (CPT), the left-hand of the function increases much more steeply than gains, thus being more "painful ...
Suppose that we are asked to bet for or against the outcome "6". We might reason that there are two relevant outcomes here "6" or "not 6", and that these are mutually exclusive and exhaustive. A common fallacy is assigning the probability 1/2 to each of the two outcomes, when "not 6" is five times more likely than "6."
The modern proof of the strong law is more complex than that of the weak law, and relies on passing to an appropriate subsequence. [17] The strong law of large numbers can itself be seen as a special case of the pointwise ergodic theorem. This view justifies the intuitive interpretation of the expected value (for Lebesgue integration only) of a ...
As invoked in everyday life, the "law" usually reflects wishful thinking or a poor understanding of statistics rather than any mathematical principle. While there is a real theorem that a random variable will reflect its underlying probability over a very large sample, the law of averages typically assumes that an unnatural short-term "balance ...
Assume, for simplicity, that the total number of humans who will ever be born is 60 billion (N 1), or 6,000 billion (N 2). [6]If there is no prior knowledge of the position that a currently living individual, X, has in the history of humanity, one may instead compute how many humans were born before X, and arrive at say 59,854,795,447, which would necessarily place X among the first 60 billion ...