Ruin Probabilities - UNL Math - University of Nebraska–Lincoln
... at some position T0 . The person takes a step to the right to T0 + 1 with probability p and takes a step to the left to T0 − 1 with probability q and continues this random process. Then instead of the total fortune at any time, we consider the geometric position on the line at any time. Instead of r ...
... at some position T0 . The person takes a step to the right to T0 + 1 with probability p and takes a step to the left to T0 − 1 with probability q and continues this random process. Then instead of the total fortune at any time, we consider the geometric position on the line at any time. Instead of r ...
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... This notes is ment to be a review of some basic inequalities and bounds on Random variables. A basic understanding of probability theory and set algebra might be required of the reader. This document is aimed to provide clear and complete proof for some inequalities. For readers familiar with the to ...
... This notes is ment to be a review of some basic inequalities and bounds on Random variables. A basic understanding of probability theory and set algebra might be required of the reader. This document is aimed to provide clear and complete proof for some inequalities. For readers familiar with the to ...
Probability of One Event
... where all the possible outcomes are equally likely. For example, when you roll a fair dice you are equally likely to get any of the six numbers. (The words 'fair' or 'unbiased' mean that all outcomes are equally likely.) number of successful outcomes total number of outcomes ...
... where all the possible outcomes are equally likely. For example, when you roll a fair dice you are equally likely to get any of the six numbers. (The words 'fair' or 'unbiased' mean that all outcomes are equally likely.) number of successful outcomes total number of outcomes ...
6= BPP on the hardness of PAC learning On basing ZK
... Throughout this paper we say learning is hard if every non-uniform algorithm (equivalently family of circuits) fails to learn the concept class of functions computable by circuits of size n2 under the uniform input distribution1 on all but finitely many input lengths, given access to an example orac ...
... Throughout this paper we say learning is hard if every non-uniform algorithm (equivalently family of circuits) fails to learn the concept class of functions computable by circuits of size n2 under the uniform input distribution1 on all but finitely many input lengths, given access to an example orac ...
1 Kroesus and the oracles
... was independent of whether the oracle made correct guesses at other questions and also that differ- ...
... was independent of whether the oracle made correct guesses at other questions and also that differ- ...
A Simplex Algorithm Whose Average Number of Steps Is Bounded
... probability of a basis to occur in the solution process. The upper bounds for these cases are then analyzed in two pairs in Sections 5 and 6. In Section 7 we prove the lower bound result. The specific upper and lower bounds are summarized in Section 8. 2. The Probabilistic Model ...
... probability of a basis to occur in the solution process. The upper bounds for these cases are then analyzed in two pairs in Sections 5 and 6. In Section 7 we prove the lower bound result. The specific upper and lower bounds are summarized in Section 8. 2. The Probabilistic Model ...
Context-specific approximation in probabilistic inference
... parents. It seems more plausible that in some contexts the value of the parent doesn't make much difference. The general idea is to simplify the network, by ignoring distinctions that don't make much difference in the con ditional probability, but what may be ignored may change from context to cont ...
... parents. It seems more plausible that in some contexts the value of the parent doesn't make much difference. The general idea is to simplify the network, by ignoring distinctions that don't make much difference in the con ditional probability, but what may be ignored may change from context to cont ...
Stochasticity, invasions, and branching random walks
... Spatial models are extraordinarily varied (Kareiva, 1990; Keeling, 1999). Ecologists have long used simple deterministic models, such as reaction–diffusion equations, to study persistence, spread, and other spatial phenomena (Skellam, 1951; Kierstead and Slobodkin, 1953; Okubo and Levin, 2001). More ...
... Spatial models are extraordinarily varied (Kareiva, 1990; Keeling, 1999). Ecologists have long used simple deterministic models, such as reaction–diffusion equations, to study persistence, spread, and other spatial phenomena (Skellam, 1951; Kierstead and Slobodkin, 1953; Okubo and Levin, 2001). More ...
Statistics of the Environment? - RuCCS
... This conception implies that probability is an objective characteristic of external events, and psychologists absorbed this assumption along with their t-tests and ANOVAs. More specifically, many cognitive psychologists first encountered the notion of a Bayesian prior in the context of the “base rat ...
... This conception implies that probability is an objective characteristic of external events, and psychologists absorbed this assumption along with their t-tests and ANOVAs. More specifically, many cognitive psychologists first encountered the notion of a Bayesian prior in the context of the “base rat ...
Probability box
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A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.