alternative probability Chapter - Department of Statistics
... number of factors such as which way up it started, the degree of spin, the speed and angle with which it left the thumb and how far it has to fall. If we knew all this, then, with sufficient expertise in physics, we could write down some equations which are thought to govern the motion of the coin ( ...
... number of factors such as which way up it started, the degree of spin, the speed and angle with which it left the thumb and how far it has to fall. If we knew all this, then, with sufficient expertise in physics, we could write down some equations which are thought to govern the motion of the coin ( ...
TRAINING SCHOOL TEACHERS TO TEACH PROBABILITY
... had a dual character since its emergence: a statistical side was concerned with stochastic rules of random processes, while the epistemic side views probability as a degree of belief. This duality was present in many of the authors who contribute to progress in the field. For example, while Pascal’s ...
... had a dual character since its emergence: a statistical side was concerned with stochastic rules of random processes, while the epistemic side views probability as a degree of belief. This duality was present in many of the authors who contribute to progress in the field. For example, while Pascal’s ...
A Probability Paradox
... is always able to find some door to be door B, how can the opening of door B say anything about door A? Hence, its probability must still be 1/3. Since door C is the only remaining door, its success probability must then be 2/3. Amazingly, this still did not convince our three distinguished friends. ...
... is always able to find some door to be door B, how can the opening of door B say anything about door A? Hence, its probability must still be 1/3. Since door C is the only remaining door, its success probability must then be 2/3. Amazingly, this still did not convince our three distinguished friends. ...
Members of random closed sets - University of Hawaii Mathematics
... A starting point for the present paper was the observation (*) that each nonDNR Turing degree is Low(ML, Kurtz). A proof of this result due and credited to Kjos-Hanssen is given by Greenberg and Miller [4]; they prove that the converse holds as well. This can be used to show that each slow point (se ...
... A starting point for the present paper was the observation (*) that each nonDNR Turing degree is Low(ML, Kurtz). A proof of this result due and credited to Kjos-Hanssen is given by Greenberg and Miller [4]; they prove that the converse holds as well. This can be used to show that each slow point (se ...
A PROBABILISTIC SCHEME WITH UNIFORM CORRELATION
... event A (success) in k series of nj trials each with j = 1, 2, …, k, we introduce at this point the assumption of dependence between the nj trials of each series, maintaining the assumption of independence between the k series, though. Since the following analysis focuses on the relationships of dep ...
... event A (success) in k series of nj trials each with j = 1, 2, …, k, we introduce at this point the assumption of dependence between the nj trials of each series, maintaining the assumption of independence between the k series, though. Since the following analysis focuses on the relationships of dep ...
Lecture 10: Pseudorandom Generators (Sep 29, Karn Seth)
... A first attempt at constructing a PRG was made by Shamir, as follows: Let f be a OWP. Then construct g(s) = f m (s)||f m−1 (s)|| . . . ||f (s)||s. It is easy to see that this function fails the pseudorandomness property, by considering the distinguisher D that, on input (1n , y), considers the last ...
... A first attempt at constructing a PRG was made by Shamir, as follows: Let f be a OWP. Then construct g(s) = f m (s)||f m−1 (s)|| . . . ||f (s)||s. It is easy to see that this function fails the pseudorandomness property, by considering the distinguisher D that, on input (1n , y), considers the last ...
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.