Part e - Department of Computer Science
... Thm. If the probability that a randomly selected element of the set S does not have a particular property is less than 1, then there exists an element in S with this property. Alternatively: If the probability that a random element of S has a particular property is larger than 0, then there exists a ...
... Thm. If the probability that a randomly selected element of the set S does not have a particular property is less than 1, then there exists an element in S with this property. Alternatively: If the probability that a random element of S has a particular property is larger than 0, then there exists a ...
Data analysis: Frequently Bayesian
... For frequentists, a probability is something associated with the outcome of an observation that is at least in principle repeatable, such as the number of nuclei that decay in a certain time. After many repetitions of a measurement under the same conditions, the fraction of times one sees a certain ...
... For frequentists, a probability is something associated with the outcome of an observation that is at least in principle repeatable, such as the number of nuclei that decay in a certain time. After many repetitions of a measurement under the same conditions, the fraction of times one sees a certain ...
peA) P(BI and A)
... Equation (2.5) is called Bayes' law, also known as Bayes' rule or Bayes' theorem. Bayes' law is a simple, almost trivial, mathematical result, but its implications are profound. In fact, there is an entire branch of statistics, called Bayesian statistics, that is based upon Bayes' law and is now pla ...
... Equation (2.5) is called Bayes' law, also known as Bayes' rule or Bayes' theorem. Bayes' law is a simple, almost trivial, mathematical result, but its implications are profound. In fact, there is an entire branch of statistics, called Bayesian statistics, that is based upon Bayes' law and is now pla ...
Probability
... The probability of a total greater than 8 given that the first die is 6 is 4/6 = 2/3. More formally, this probability can be written as: p(total>8 | Die 1 = 6) = 2/3(6,3; 6,4; 6,5; 6,6). Conditional probability using “Probability Type ...
... The probability of a total greater than 8 given that the first die is 6 is 4/6 = 2/3. More formally, this probability can be written as: p(total>8 | Die 1 = 6) = 2/3(6,3; 6,4; 6,5; 6,6). Conditional probability using “Probability Type ...
Computation of the Probability of Initial Substring Generation by
... Probabilistic methods have been shown most effective in automatic speech recognition. Recognition (actually transcription) of natural unrestricted speech requires a "language model" that attaches probabilities to the production of all possible strings of words (Bahl et al. 1983). Consequently, if we ...
... Probabilistic methods have been shown most effective in automatic speech recognition. Recognition (actually transcription) of natural unrestricted speech requires a "language model" that attaches probabilities to the production of all possible strings of words (Bahl et al. 1983). Consequently, if we ...
Probability myths
... Note this works out because there are 5 odd digits and 5 even digits (including 0), so the probability of choosing an odd number is exactly the probability of getting heads (0.5), and the probability of choosing an even number is exactly the same as the probability of getting tails (0.5 again). ...
... Note this works out because there are 5 odd digits and 5 even digits (including 0), so the probability of choosing an odd number is exactly the probability of getting heads (0.5), and the probability of choosing an even number is exactly the same as the probability of getting tails (0.5 again). ...
Lecture 2
... A California study concluded that by following 7 simple heath rules, a man’s life can be extended by 11 years on the average and a woman’s life by 7 years. These 7 rules are: no smoking, regular exercise, use alcohol moderately, get 7 to 8 hours of sleep, maintain proper weight, eat breakfast, and d ...
... A California study concluded that by following 7 simple heath rules, a man’s life can be extended by 11 years on the average and a woman’s life by 7 years. These 7 rules are: no smoking, regular exercise, use alcohol moderately, get 7 to 8 hours of sleep, maintain proper weight, eat breakfast, and d ...
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.