Additive factors and stages of mental processes in - Purdue e-Pubs
... If all the processes are sequential, we say the processes are in series. In that case if a certain process is prolonged by some amount the response time will increase by that amount. The situation is more complicated when concurrent processes are present, but their presence makes effects of factors ...
... If all the processes are sequential, we say the processes are in series. In that case if a certain process is prolonged by some amount the response time will increase by that amount. The situation is more complicated when concurrent processes are present, but their presence makes effects of factors ...
Continuum Probability and Sets of Measure Zero
... So far, we have identified B with the interval of real numbers I and have introduced the desirability of a general way to measure the sizes of sets in I and some properties that such a measure should have. The next step is to assign a system for computing probabilities of events in B using the measu ...
... So far, we have identified B with the interval of real numbers I and have introduced the desirability of a general way to measure the sizes of sets in I and some properties that such a measure should have. The next step is to assign a system for computing probabilities of events in B using the measu ...
The Time Scale of Evolutionary Innovation
... There are many results that characterize single steps in terms of the fixation time of new mutants arising in populations of certain size and structure. But here we ask a different question, which is concerned with the much longer time scale of evolutionary trajectories: how long does it take for a ...
... There are many results that characterize single steps in terms of the fixation time of new mutants arising in populations of certain size and structure. But here we ask a different question, which is concerned with the much longer time scale of evolutionary trajectories: how long does it take for a ...
Survival probabilities of weighted random walks
... Proposition 2.12. Unfortunately, an explicit computation of λβ does not seem to be possible easily. 1.3. Related work. Let us briefly summarize some important known results on survival probabilities. For Brownian motion, the survival exponent is easily seen to be θ = 1/2 by the reflection principle. ...
... Proposition 2.12. Unfortunately, an explicit computation of λβ does not seem to be possible easily. 1.3. Related work. Let us briefly summarize some important known results on survival probabilities. For Brownian motion, the survival exponent is easily seen to be θ = 1/2 by the reflection principle. ...
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.