4 Sums of Independent Random Variables
... Definition 4.12. The sequence S n = ni=1 X i is said to be a nearest neighbor random walk (or a p-q random walk) on the integers if the random variables X i are independent, identically distributed and have common distribution P {X i = +1} = 1 ° P {X i = °1} = p = 1 ° q. If p = 1/2 then S n is calle ...
... Definition 4.12. The sequence S n = ni=1 X i is said to be a nearest neighbor random walk (or a p-q random walk) on the integers if the random variables X i are independent, identically distributed and have common distribution P {X i = +1} = 1 ° P {X i = °1} = p = 1 ° q. If p = 1/2 then S n is calle ...
Optimal Illusion of Control and Related Perception Biases - cerge-ei
... 2016, GAMES 2016 and the Limited Cognition workshop in Barcelona for comments. Ludmila Matysková has provided excellent research assistance and Judith Levi has carefully edited the text. ...
... 2016, GAMES 2016 and the Limited Cognition workshop in Barcelona for comments. Ludmila Matysková has provided excellent research assistance and Judith Levi has carefully edited the text. ...
cern_stat_3
... Suppose we toss the coin N = 20 times and get n = 17 heads. Region of data space with equal or lesser compatibility with H relative to n = 17 is: n = 17, 18, 19, 20, 0, 1, 2, 3. Adding up the probabilities for these values gives: ...
... Suppose we toss the coin N = 20 times and get n = 17 heads. Region of data space with equal or lesser compatibility with H relative to n = 17 is: n = 17, 18, 19, 20, 0, 1, 2, 3. Adding up the probabilities for these values gives: ...
Chapter 5 - Pearson Higher Education
... the proportion of heads fluctuates wildly around 0.5, but as the number of flips increases, the proportion of heads settles down near 0.5. Jakob Bernoulli (a major contributor to the field of probability) believed that the Law of Large Numbers was common sense. This is evident in the following quote ...
... the proportion of heads fluctuates wildly around 0.5, but as the number of flips increases, the proportion of heads settles down near 0.5. Jakob Bernoulli (a major contributor to the field of probability) believed that the Law of Large Numbers was common sense. This is evident in the following quote ...
this one (Raghavendra, Schramm)
... the planted clique problem for some k < n? While lower bounds are known for Lovász-Schrijver SDP relaxations for planted clique [FK00, FK03], SOS relaxations can in general be much more powerful than Lovász-Schrijver relaxations. For example, while there are instances of unique games that are hard ...
... the planted clique problem for some k < n? While lower bounds are known for Lovász-Schrijver SDP relaxations for planted clique [FK00, FK03], SOS relaxations can in general be much more powerful than Lovász-Schrijver relaxations. For example, while there are instances of unique games that are hard ...
Lecture Notes for Introductory Probability
... The probability of this is 4 times the probability of getting a 6 in a single die, i.e., 4/6 = 2/3; clearly I had an advantage and indeed I was making money. Now I bet even money that within 24 rolls of two dice I get at least one double 6. This has the same advantage (24/62 = 2/3), but now I am los ...
... The probability of this is 4 times the probability of getting a 6 in a single die, i.e., 4/6 = 2/3; clearly I had an advantage and indeed I was making money. Now I bet even money that within 24 rolls of two dice I get at least one double 6. This has the same advantage (24/62 = 2/3), but now I am los ...
pdf
... that level. One then fixes such a restriction for that level and continues to the next level. To obtain a lower bound, one chooses a family of restrictions suited to the target of the analysis. In the case of P HPnm , the natural restrictions to consider correspond to partial matchings between pigeo ...
... that level. One then fixes such a restriction for that level and continues to the next level. To obtain a lower bound, one chooses a family of restrictions suited to the target of the analysis. In the case of P HPnm , the natural restrictions to consider correspond to partial matchings between pigeo ...
Decomposition of Event Sequences into Independent Components
... tion. The algorithms were implemented under Matlab and a large number of event sequence analysis routines and visualization tools were written. The area of decomposing sequences of events seems to be new to data mining. There are, of course, several topics in which related issues have been considere ...
... tion. The algorithms were implemented under Matlab and a large number of event sequence analysis routines and visualization tools were written. The area of decomposing sequences of events seems to be new to data mining. There are, of course, several topics in which related issues have been considere ...
StochModels Lecture 3: Probability Metrics
... ⇒ If a given number of characteristics of two discrete random variables with finitely many outcomes agree, then their distribution functions agree completely. Then, instead of trying to figure out how many characteristics to include in a metric of a given type, is it possible to consider ways of mea ...
... ⇒ If a given number of characteristics of two discrete random variables with finitely many outcomes agree, then their distribution functions agree completely. Then, instead of trying to figure out how many characteristics to include in a metric of a given type, is it possible to consider ways of mea ...
Numerical integration for complicated functions and random
... and Ulam, as soon as electronic computer was born. It was also the birth of the problem ‘How do we realize random sampling by computer?’ In 1960’s, Kolmogorov, Chaitin and others began the theory of random numbers ([8, 16]), known as ‘Kolmogorov’s complexity theory’, by using the theory of computati ...
... and Ulam, as soon as electronic computer was born. It was also the birth of the problem ‘How do we realize random sampling by computer?’ In 1960’s, Kolmogorov, Chaitin and others began the theory of random numbers ([8, 16]), known as ‘Kolmogorov’s complexity theory’, by using the theory of computati ...
The researcher and the consultant: a dialogue on null hypothesis
... alpha to a lower value after the fact to make the test result appear more impressive [9] (irritation #9). Consultant You are right. This is an unfortunate mixture of Neyman and Pearson’s NHT and Fisher’s ST that has evolved over the years [7]. It has several variants and is constantly mutating, but ...
... alpha to a lower value after the fact to make the test result appear more impressive [9] (irritation #9). Consultant You are right. This is an unfortunate mixture of Neyman and Pearson’s NHT and Fisher’s ST that has evolved over the years [7]. It has several variants and is constantly mutating, but ...
Chapter 4. Method of Maximum Likelihood
... In these conditions the limits of what is computationally feasible are spontaneously observed. Until quite recently these limits were set by the capacity of the human calculator, equipped with pencil and paper and with such aids as the slide rule, tables of logarithms, and other convenient tables, w ...
... In these conditions the limits of what is computationally feasible are spontaneously observed. Until quite recently these limits were set by the capacity of the human calculator, equipped with pencil and paper and with such aids as the slide rule, tables of logarithms, and other convenient tables, w ...
(pdf)
... to denote the integral of f over B with respect to Lebesgue measure. Definition 1.5. Let µ be a probability measure on Bd . If f : Rd → R is measurable R such that for all B ∈ Bd we have µ(B) = B f (x)dx, we say f is a density function for µ. It is clear that any measurable fR : Rd → R can only be a ...
... to denote the integral of f over B with respect to Lebesgue measure. Definition 1.5. Let µ be a probability measure on Bd . If f : Rd → R is measurable R such that for all B ∈ Bd we have µ(B) = B f (x)dx, we say f is a density function for µ. It is clear that any measurable fR : Rd → R can only be a ...
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.