
Perceptions of Randomness: Why Three Heads Are Better Than Four
... misperception has likewise been attributed to the belief that local and global sequences should share the same properties: Black on the next trial would “result in a more representative sequence than the occurrence of an additional red” (Tversky, 1974, p. 151). This set of errors and biases is one o ...
... misperception has likewise been attributed to the belief that local and global sequences should share the same properties: Black on the next trial would “result in a more representative sequence than the occurrence of an additional red” (Tversky, 1974, p. 151). This set of errors and biases is one o ...
Preschoolers sample from probability distributions
... children’s responses reflected probability matching (70% providing the more probable chip response). That is, results suggest that children were not simply randomly guessing, as responses were significantly different from chance (p < .05; binomial test), but not significantly different from the pred ...
... children’s responses reflected probability matching (70% providing the more probable chip response). That is, results suggest that children were not simply randomly guessing, as responses were significantly different from chance (p < .05; binomial test), but not significantly different from the pred ...
Slides - RAD Lab - University of California, Berkeley
... customer sitting at?) • Problem: in many problem domains we have a very large (combinatorial) number of possible tables – using the Dirichlet process means having a large number of parameters, which may overfit – perhaps instead want to characterize objects as collections of attributes (“sparse feat ...
... customer sitting at?) • Problem: in many problem domains we have a very large (combinatorial) number of possible tables – using the Dirichlet process means having a large number of parameters, which may overfit – perhaps instead want to characterize objects as collections of attributes (“sparse feat ...
Notes on Zero Knowledge 1 Interactive Proofs
... Definition 6 (Honest Verifier Zero Knowledge) A honest verifier Perfect Zero Knowledge proof system for a language L is an interactive proof (VL , PL ) for L, as defined in the previous section, such that there is a probabilistic algorithm S (for Simulator) that runs in average polynomial time and s ...
... Definition 6 (Honest Verifier Zero Knowledge) A honest verifier Perfect Zero Knowledge proof system for a language L is an interactive proof (VL , PL ) for L, as defined in the previous section, such that there is a probabilistic algorithm S (for Simulator) that runs in average polynomial time and s ...
Chapter 16 Skills Practice
... 4. Suppose that you write the letters A, B, C, and D on four equal-size slips of paper. Then, you put them in a bag and choose one slip from the bag without looking. You repeat this 40 times and record the results shown in the table. Note that you always put the slip you chose back into the bag ...
... 4. Suppose that you write the letters A, B, C, and D on four equal-size slips of paper. Then, you put them in a bag and choose one slip from the bag without looking. You repeat this 40 times and record the results shown in the table. Note that you always put the slip you chose back into the bag ...
Table of contents, introduction, and review of probability
... going back and forth between a mathematical model and a real-world problem. In doing research, we grope toward results, and successful groping requires both a strong intuition and precise reasoning. The text neither uses nor develops measure theory. Measure theory is undoubtedly important in underst ...
... going back and forth between a mathematical model and a real-world problem. In doing research, we grope toward results, and successful groping requires both a strong intuition and precise reasoning. The text neither uses nor develops measure theory. Measure theory is undoubtedly important in underst ...
Probability of Precipitation: POP What is the Chance That People
... 1. Survey questions on ranking should have been in random order. 2. Surveys should have referred to “percentage rain”, rather than ...
... 1. Survey questions on ranking should have been in random order. 2. Surveys should have referred to “percentage rain”, rather than ...
CHAPTER III - MARKOV CHAINS 1. General Theory of Markov
... Hence limn→∞ Zn exists with probability 1, and it is easy to see that the limit must ...
... Hence limn→∞ Zn exists with probability 1, and it is easy to see that the limit must ...
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.