Probability Probability: A measure of the chance that something will
... A popular gambling game called craps is described below. A player rolls two dice, and the sum of the two numbers that appear is recorded. If the sum on the first roll is 7 or 11, the player wins immediately and the game stops. If on the first attempt a sum of 2, or 3, or 12 is scored, the player los ...
... A popular gambling game called craps is described below. A player rolls two dice, and the sum of the two numbers that appear is recorded. If the sum on the first roll is 7 or 11, the player wins immediately and the game stops. If on the first attempt a sum of 2, or 3, or 12 is scored, the player los ...
Lecture Notes
... We say that a distribution passes the next-bit test if no efficient adversary can, given any prefix of a sequence sampled from the distribution, predict the next bit in the sequence with probability significantely better than 12 (recall that this was one of the test originally suggested in the intro ...
... We say that a distribution passes the next-bit test if no efficient adversary can, given any prefix of a sequence sampled from the distribution, predict the next bit in the sequence with probability significantely better than 12 (recall that this was one of the test originally suggested in the intro ...
part2s - NYU Stern School of Business
... (a random variable) represent the result of a particular reservation. That is, we could assign a value of 1 to X if the person shows up for the flight (X = 1), and let X = 0 if the person does not. Then, P(X = 0) = 1 - p and P(X = 1) = p. This is an example of a Bernoulli process, named for the Swis ...
... (a random variable) represent the result of a particular reservation. That is, we could assign a value of 1 to X if the person shows up for the flight (X = 1), and let X = 0 if the person does not. Then, P(X = 0) = 1 - p and P(X = 1) = p. This is an example of a Bernoulli process, named for the Swis ...
Student Study Guide
... 5. The test consists of ten questions: five multiple-choice questions worth 5 points each and five computation problems worth 15 points each. 6. The test will cover all material covered in class up to Chapter 6. The first five problems on the test will concern concepts, not calculations. These probl ...
... 5. The test consists of ten questions: five multiple-choice questions worth 5 points each and five computation problems worth 15 points each. 6. The test will cover all material covered in class up to Chapter 6. The first five problems on the test will concern concepts, not calculations. These probl ...
CS 471 - Bayesian Networks
... • Nodes: random variables (typically binary or discrete, but methods also exist to handle continuous variables) • Arcs: indicate probabilistic dependencies between nodes (lack of link signifies conditional independence) – CPD: conditional probability distribution (BN’s parameters) • Conditional prob ...
... • Nodes: random variables (typically binary or discrete, but methods also exist to handle continuous variables) • Arcs: indicate probabilistic dependencies between nodes (lack of link signifies conditional independence) – CPD: conditional probability distribution (BN’s parameters) • Conditional prob ...
Solutions
... Problem 1. Consider an experiment that consists of determining the type of job – either blue-collar or white-collar – and the political affiliation – Republican, Democratic, or Independent – of the 15 members of an adult soccer team. How many outcomes are (a) in the sample space; Each of the players ...
... Problem 1. Consider an experiment that consists of determining the type of job – either blue-collar or white-collar – and the political affiliation – Republican, Democratic, or Independent – of the 15 members of an adult soccer team. How many outcomes are (a) in the sample space; Each of the players ...
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.