Basic Probability Topics - Department of Electronic Engineering
... A random variable is a real valued function defined on the sample space. This function X = X(ω) assigns a number to each outcome ω of the experiment. Example: tossing a coin experiment ...
... A random variable is a real valued function defined on the sample space. This function X = X(ω) assigns a number to each outcome ω of the experiment. Example: tossing a coin experiment ...
Anonymity and Information Hiding in Multiagent Systems
... must be hidden. The “how well does it need to be hidden” component depends on the situation. Our definition of secrecy says that for any nontrivial fact ϕ (that is, one that is not already valid) that depends only the state of the classified or high-level agent, the formula ¬Kj ϕ must be valid. (See ...
... must be hidden. The “how well does it need to be hidden” component depends on the situation. Our definition of secrecy says that for any nontrivial fact ϕ (that is, one that is not already valid) that depends only the state of the classified or high-level agent, the formula ¬Kj ϕ must be valid. (See ...
An Analysis of Random-Walk Cuckoo Hashing
... the random-walk insertion method for cuckoo hashing. There is a clear intuition for how this random walk on the buckets should perform. If a fraction f of the items are adjacent to at least one empty bucket in the corresponding graph, then we might expect that each time we place one item and conside ...
... the random-walk insertion method for cuckoo hashing. There is a clear intuition for how this random walk on the buckets should perform. If a fraction f of the items are adjacent to at least one empty bucket in the corresponding graph, then we might expect that each time we place one item and conside ...
pdf
... an indication that some of the previous beliefs were wrong and should be discarded. It tries to choose the most plausible beliefs that can accommodate the observation. Update, on the other hand, assumes that the previous beliefs were correct, and that the observation is an indication that a change o ...
... an indication that some of the previous beliefs were wrong and should be discarded. It tries to choose the most plausible beliefs that can accommodate the observation. Update, on the other hand, assumes that the previous beliefs were correct, and that the observation is an indication that a change o ...
Nucleation and growth in two dimensions
... p stops accelerating and reaches its ‘terminal velocity’, at which it takes time Θ( n/k) to grow one step in each direction, cf. the 1-dimensional setting. The main component missing from the above heuristic is the interaction between different droplets. This is most important (and obvious) when k ≪ ...
... p stops accelerating and reaches its ‘terminal velocity’, at which it takes time Θ( n/k) to grow one step in each direction, cf. the 1-dimensional setting. The main component missing from the above heuristic is the interaction between different droplets. This is most important (and obvious) when k ≪ ...
here for U12 text. - Iowa State University
... our effort in Section 12.2 by introducing renewal theory for the ordinary renewal process, as it is the fundamental theory on which the simplest model of a repairable component is based. Section 12.3 presents the special case of the Poisson process, based on exponentially distributed inter-failure t ...
... our effort in Section 12.2 by introducing renewal theory for the ordinary renewal process, as it is the fundamental theory on which the simplest model of a repairable component is based. Section 12.3 presents the special case of the Poisson process, based on exponentially distributed inter-failure t ...
MARKOV PROCESSES WITH COUNTABLE STATE SPACES
... The analysis in this chapter is restricted almost entirely to irreducible Markov processes. The reason for this restriction is not that Markov processes with multiple classes of states are unimportant, but rather that they can usually be best understood by first looking at the embedded Markov chains ...
... The analysis in this chapter is restricted almost entirely to irreducible Markov processes. The reason for this restriction is not that Markov processes with multiple classes of states are unimportant, but rather that they can usually be best understood by first looking at the embedded Markov chains ...
... that manipulation is a more effective way than observation to induce cause (see Reichenbach, 1956, for discussion) because intervention on an independent variable limits the possible reasons for a subsequent effect. On the other hand, intervention on a variable does not support inference about the v ...
Bayesian Perceptual Psychology
... Motor efference copy figures most prominently in Bayesian models of sensorimotor control (Wolpert, 2007). ...
... Motor efference copy figures most prominently in Bayesian models of sensorimotor control (Wolpert, 2007). ...
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.