What Could Be Objective About Probabilities
... calculate. Again, they might both decay earlier than the half-life, or both later, or one earlier and one later, with calculable probabilities for each. And it is no more difficult to calculate the probabilities for any number of tritium atoms, including the total number of all tritium atoms in the ...
... calculate. Again, they might both decay earlier than the half-life, or both later, or one earlier and one later, with calculable probabilities for each. And it is no more difficult to calculate the probabilities for any number of tritium atoms, including the total number of all tritium atoms in the ...
Proceedings version
... ,,here f~ and h~ are monotone nondecreasing functions, then Find-Redundant-Set is computable in ft(IE[) +O(1) steps using IE[hl(lEI) processors. Proof. The simultaneous computation of Rank(S) and of Rank(SO{e}) for all e in E - S requires f~([E[) steps using [E[hl(IE[) processors. The determination ...
... ,,here f~ and h~ are monotone nondecreasing functions, then Find-Redundant-Set is computable in ft(IE[) +O(1) steps using IE[hl(lEI) processors. Proof. The simultaneous computation of Rank(S) and of Rank(SO{e}) for all e in E - S requires f~([E[) steps using [E[hl(IE[) processors. The determination ...
Conditioning as disintegration - Department of Statistics, Yale
... sigma-®nite B contains all singleton sets and is countably generated. Thus a disintegration of a probability measures may be thought of as resulting from a careful selection of versions of the conditional expectations (in Kolmogorov's sense), in a way that eliminates awkward complications caused by ...
... sigma-®nite B contains all singleton sets and is countably generated. Thus a disintegration of a probability measures may be thought of as resulting from a careful selection of versions of the conditional expectations (in Kolmogorov's sense), in a way that eliminates awkward complications caused by ...
Probability Distribution Function of the Internal Rate of Return in One
... stands for project life. The alternative is acceptable when ...
... stands for project life. The alternative is acceptable when ...
Ibrahim Rahimov, Ph.D., Doctor of Sciences
... represented as sums of random number of random variables or random fields. I have suggested a new approach to study such sums based on an idea of their representation as sampling sums of dependent random variables. It turned out that, if we apply this representation to simple random sums, we obtain ...
... represented as sums of random number of random variables or random fields. I have suggested a new approach to study such sums based on an idea of their representation as sampling sums of dependent random variables. It turned out that, if we apply this representation to simple random sums, we obtain ...
Paradoxes Of Probability Theory
... To remove a paradox from probability theory will require, at the very least, detailed analysis of the result and the reasoning that leads to it, showing that: (1) The result is indeed absurd. (2) The reasoning leading to it violates the rules of inference developed in Chapter 2. (3) When one obeys t ...
... To remove a paradox from probability theory will require, at the very least, detailed analysis of the result and the reasoning that leads to it, showing that: (1) The result is indeed absurd. (2) The reasoning leading to it violates the rules of inference developed in Chapter 2. (3) When one obeys t ...
Randomness
Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events (or ""trials"") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input (such as from random number generators or pseudorandom number generators), are important techniques in science, as, for instance, in computational science. By analogy, quasi-Monte Carlo methods use quasirandom number generators.Random selection is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, of say research subjects, has the same probability of being chosen then we can say the selection process is random.