Sophie Hautphenne â Research Fellow in Applied Probability
... processes. The 6th International Conference on Matrix-Analytic Methods in Stochastic Models, June 2008, Beijing, China. [6] S. Hautphenne, G. Latouche and M.-A. Remiche. Extinction probability of branching processes with catastrophes. Orbel 2008, Jan. 2008, Brussels, Belgium. [5] S. Hautphenne, G. L ...
... processes. The 6th International Conference on Matrix-Analytic Methods in Stochastic Models, June 2008, Beijing, China. [6] S. Hautphenne, G. Latouche and M.-A. Remiche. Extinction probability of branching processes with catastrophes. Orbel 2008, Jan. 2008, Brussels, Belgium. [5] S. Hautphenne, G. L ...
Math 425 Introduction to Probability Lecture 10
... Any sequence with 4 W s is a Cub win, otherwise it is a Sox win (there are at least 4 Ls). Not all sequences represent actual outcomes, nor are all sequences equally likely. Why does it not matter to extend a real Series play with phantom games? ...
... Any sequence with 4 W s is a Cub win, otherwise it is a Sox win (there are at least 4 Ls). Not all sequences represent actual outcomes, nor are all sequences equally likely. Why does it not matter to extend a real Series play with phantom games? ...
The Modelling of Random Phenomena
... this random variable is equal in law to the time when the first arrival takes place. The event {T > t} means to have 0 arrivals in [0, t], whose probability according to (2) is exp{−λ t}. We observe that this probability is nonzero for all t ≥ 0, and that it cannot be expressed as the sum of the pro ...
... this random variable is equal in law to the time when the first arrival takes place. The event {T > t} means to have 0 arrivals in [0, t], whose probability according to (2) is exp{−λ t}. We observe that this probability is nonzero for all t ≥ 0, and that it cannot be expressed as the sum of the pro ...
Response Latencies and Probabilities
... In that part of mathematical psychology and economics concerned with choice behavior, far more attention has been given to the probability patterns exhibited by the responses than to the other equally obvious response measure, the response latency. From time to time papers have appeared in which a g ...
... In that part of mathematical psychology and economics concerned with choice behavior, far more attention has been given to the probability patterns exhibited by the responses than to the other equally obvious response measure, the response latency. From time to time papers have appeared in which a g ...
A short introduction to probability for statistics
... 6. There are 36 su h pairs, so any out ome ...
... 6. There are 36 su h pairs, so any out ome ...
Rational Expectations and Ambiguity: A Comment on Abel
... assumption, Abel defines a pessimist as a decision maker whose subjective probabilistic belief about asset returns is stochastically dominated by the objective distribution of these returns. Accordingly, a decision maker is characterized by doubt if her subjective probabilistic belief about asset re ...
... assumption, Abel defines a pessimist as a decision maker whose subjective probabilistic belief about asset returns is stochastically dominated by the objective distribution of these returns. Accordingly, a decision maker is characterized by doubt if her subjective probabilistic belief about asset re ...
Inclusion exclusion principle
... of Eratosthenes), the formula arising doesn't offer useful content because the number of terms in it is excessive. If each term individually can be estimated accurately, the accumulation of errors may imply that the inclusion–exclusion formula isn't directly applicable. In number theory, this diffic ...
... of Eratosthenes), the formula arising doesn't offer useful content because the number of terms in it is excessive. If each term individually can be estimated accurately, the accumulation of errors may imply that the inclusion–exclusion formula isn't directly applicable. In number theory, this diffic ...
How to Make a Difference - Measures of Voting Power Revamped
... In order to get started, we provide an argument that motivates the standard approach to measure voting power – it leads to the Banzhaf measure of voting power and a generalization thereof. Our claim is not that this reconstruction captures the actual train of thoughts that lead to the Banzhaf measur ...
... In order to get started, we provide an argument that motivates the standard approach to measure voting power – it leads to the Banzhaf measure of voting power and a generalization thereof. Our claim is not that this reconstruction captures the actual train of thoughts that lead to the Banzhaf measur ...
Weighted Sets of Probabilities and Minimax Weighted Expected
... However, Pr1 | E places uniform probability on all states where the first 100 cakes are good, and there is exactly one broken cake among the last 900. Similarly, Pr10 | E places uniform probability on all states where the first 100 cakes are good, and there are exactly ten broken cakes among the las ...
... However, Pr1 | E places uniform probability on all states where the first 100 cakes are good, and there is exactly one broken cake among the last 900. Similarly, Pr10 | E places uniform probability on all states where the first 100 cakes are good, and there are exactly ten broken cakes among the las ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.