Philosophies of Probability
... V consists of repeatable variables A and B, where A stands for age of vehicles selected at random in London in 2010 and B stands for breakdown in the last year of vehicles selected at random in London in 2010, then V determines a repeatable experiment, namely the selection of vehicles at random in L ...
... V consists of repeatable variables A and B, where A stands for age of vehicles selected at random in London in 2010 and B stands for breakdown in the last year of vehicles selected at random in London in 2010, then V determines a repeatable experiment, namely the selection of vehicles at random in L ...
Ch6 - People
... that is, either there are infinitely many zero bn ’s or the limit (6.3) diverges or the limit (6.3) converges to zero. In this latter case, we say that the infinite product diverges to zero. ...
... that is, either there are infinitely many zero bn ’s or the limit (6.3) diverges or the limit (6.3) converges to zero. In this latter case, we say that the infinite product diverges to zero. ...
- ESAIM: Proceedings
... Let Zn denote the number of vertices (also called particles or individuals) in the n-th generation, then Zn = mn , ∀n ≥ 0. In probability theory, we often encounter trees where the number of offspring of a vertex is random. The easiest case is when these random numbers are i.i.d., which leads to a G ...
... Let Zn denote the number of vertices (also called particles or individuals) in the n-th generation, then Zn = mn , ∀n ≥ 0. In probability theory, we often encounter trees where the number of offspring of a vertex is random. The easiest case is when these random numbers are i.i.d., which leads to a G ...
Probability metrics applied to problems in portfolio theory
... and all their applications. A well-known example is the celebrated Central Limit Theorem (CLT), the Generalized CLT, the max-stable CLT, functional limit theorems, etc. In general, the applicability of the limit theorems stems from the fact that the limit law can be regarded as an approximation to t ...
... and all their applications. A well-known example is the celebrated Central Limit Theorem (CLT), the Generalized CLT, the max-stable CLT, functional limit theorems, etc. In general, the applicability of the limit theorems stems from the fact that the limit law can be regarded as an approximation to t ...
Statistics of the Environment? - RuCCS
... countless textbooks and even popular media,8 the terms base rate and prior probability are explicitly treated as synonymous. The general presumption is that the frequency in the population defines an objectively correct prior that ought to be adopted by any rational observer. Later, this notion of p ...
... countless textbooks and even popular media,8 the terms base rate and prior probability are explicitly treated as synonymous. The general presumption is that the frequency in the population defines an objectively correct prior that ought to be adopted by any rational observer. Later, this notion of p ...
Random Number Generation
... number successively higher or lower than adjacent numbers several numbers above the mean followed by several numbers below the mean ...
... number successively higher or lower than adjacent numbers several numbers above the mean followed by several numbers below the mean ...
Coherent conditional probabilities and proper scoring rules
... Using the same symbols for the events and their indicators, with the pair (Fn , Pn ) we associate the random gain n X G= si Hi (Ei − pi ) , i=1 ...
... Using the same symbols for the events and their indicators, with the pair (Fn , Pn ) we associate the random gain n X G= si Hi (Ei − pi ) , i=1 ...
Countable or Uncountable*That is the question!
... If A is a countably infinite set and B is a subset of A then B is countable. Case I: If B is the empty set or a finite set then B is countable. Case II: B is an infinite set Since A is countable we can write the elements of A in the order a1, a2, a3, . . . If B is a subset of A then an infinite num ...
... If A is a countably infinite set and B is a subset of A then B is countable. Case I: If B is the empty set or a finite set then B is countable. Case II: B is an infinite set Since A is countable we can write the elements of A in the order a1, a2, a3, . . . If B is a subset of A then an infinite num ...
A note on random number generation
... At the beginning of the nineties, there was no state-of-the-art algorithms to generate pseudo random numbers. And the article of Park & Miller (1988) entitled Random generators: good ones are hard to find is a clear proof. Despite this fact, most users thought the rand function they used was good, b ...
... At the beginning of the nineties, there was no state-of-the-art algorithms to generate pseudo random numbers. And the article of Park & Miller (1988) entitled Random generators: good ones are hard to find is a clear proof. Despite this fact, most users thought the rand function they used was good, b ...
Arguments for–or against–Probabilism?
... Here, ‘the probability calculus’ refers to at least the finite fragment of Kolmogorov’s theory, according to which probabilities are non-negative, normalized (with a top value of 1), and finitely additive. Probabilism is a simple, fecund theory. Indeed, it achieves such an elegant balance of simplicit ...
... Here, ‘the probability calculus’ refers to at least the finite fragment of Kolmogorov’s theory, according to which probabilities are non-negative, normalized (with a top value of 1), and finitely additive. Probabilism is a simple, fecund theory. Indeed, it achieves such an elegant balance of simplicit ...
Links Between Theoretical and Effective Differential Probabilities
... have been designed to be resistant to the basic differential cryptanalysis. Nevertheless, when a new cipher is proposed, cryptanalysts try to mount the best possible linear and differential attacks. In the case of PRESENT[BKL+ 07], the cipher we used for the experiments, the actual best published di ...
... have been designed to be resistant to the basic differential cryptanalysis. Nevertheless, when a new cipher is proposed, cryptanalysts try to mount the best possible linear and differential attacks. In the case of PRESENT[BKL+ 07], the cipher we used for the experiments, the actual best published di ...
Weighted Sets of Probabilities and Minimax Weighted Expected
... update probabilities, using likelihood (see below). On the other hand, these weights do not act like probabilities if the set of probabilities is infinite. For example, if we had a countable set of hypotheses, we could assign them all weight 1 (so that, intuitively, they are all viewed as equally li ...
... update probabilities, using likelihood (see below). On the other hand, these weights do not act like probabilities if the set of probabilities is infinite. For example, if we had a countable set of hypotheses, we could assign them all weight 1 (so that, intuitively, they are all viewed as equally li ...
Sets, Infinity, and Mappings - University of Southern California
... b) Use part (a) to prove that z is irrational. Hint: A number is rational if and only if its decimal expansion has an eventually repeating pattern. Suppose {a11 , a22 , a33 , . . .} has an eventually repeating pattern. G. Infinite levels of infinity A finite set A has strictly smaller cardinality th ...
... b) Use part (a) to prove that z is irrational. Hint: A number is rational if and only if its decimal expansion has an eventually repeating pattern. Suppose {a11 , a22 , a33 , . . .} has an eventually repeating pattern. G. Infinite levels of infinity A finite set A has strictly smaller cardinality th ...
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.In this context, ""almost surely"" is a mathematical term with a precise meaning, and the ""monkey"" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the ""monkey metaphor"" is that of French mathematician Émile Borel in 1913, but the first instance may be even earlier. The relevance of the theorem is questionable—the probability of a universe full of monkeys typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). It should also be noted that real monkeys don't produce uniformly random output, which means that an actual monkey hitting keys for an infinite amount of time has no statistical certainty of ever producing any given text.Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic simians and typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.