LECTURE 8 (Week 2)
... The gambling industry relies on probability distributions to calculate the odds of winning. The rewards are then fixed precisely so that, on average, players lose and the house wins. The industry is very tough on so-called “cheaters” because their probability to win exceeds that of the house. Remem ...
... The gambling industry relies on probability distributions to calculate the odds of winning. The rewards are then fixed precisely so that, on average, players lose and the house wins. The industry is very tough on so-called “cheaters” because their probability to win exceeds that of the house. Remem ...
probability - Kuwait University - College of Business Administration
... 4. Suppose A and B are independent events where P(A) = 0.4 and P(B) =0.5. Then P(A|B)=0.5 5. If P(A) = 0.4 and P(A|B) = 0.5, then there is a 20% chance that A and B Occur at the same time. 6. Hamad and Fahd go to a coffee shop during their lunch break. Each one of them wants to pay. They decided to ...
... 4. Suppose A and B are independent events where P(A) = 0.4 and P(B) =0.5. Then P(A|B)=0.5 5. If P(A) = 0.4 and P(A|B) = 0.5, then there is a 20% chance that A and B Occur at the same time. 6. Hamad and Fahd go to a coffee shop during their lunch break. Each one of them wants to pay. They decided to ...
samples
... variables that are enforced by this Bayesian network, using the notation A B to mean that A is independent of B. (b) Write down three independencies which do not necessarily hold in this Bayesian network. (c) Write down all the conditional independencies that are enforced by this Bayesian network, u ...
... variables that are enforced by this Bayesian network, using the notation A B to mean that A is independent of B. (b) Write down three independencies which do not necessarily hold in this Bayesian network. (c) Write down all the conditional independencies that are enforced by this Bayesian network, u ...
probability of an event - hedge fund analysis
... the long-run relative frequency with which outcomes occur. The probabilities represent estimates from the sample and improve with larger sample sizes. When it is not reasonable to use the classical approach and there is not history of outcomes (or too short a history), the subjective approach is emp ...
... the long-run relative frequency with which outcomes occur. The probabilities represent estimates from the sample and improve with larger sample sizes. When it is not reasonable to use the classical approach and there is not history of outcomes (or too short a history), the subjective approach is emp ...
Topic #5: Probability
... exist in the nature of reality itself, particularly in quantum phenomena governed by Heisenberg's uncertainty principle. Although the same mathematical rules apply regardless of which interpretation is chosen, the choice has major implications for the way in which probability is used to model the re ...
... exist in the nature of reality itself, particularly in quantum phenomena governed by Heisenberg's uncertainty principle. Although the same mathematical rules apply regardless of which interpretation is chosen, the choice has major implications for the way in which probability is used to model the re ...
1. The discrete random variable X has a PMF described by the table
... C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A and B = (3} A and C = {2, 3, 5, 7} B and C = {3, 6, 9} P(A) = 8/20 = .4 P(B) = 6/20 = .3 P(C) = 10/20 = .5 P(A and B) = 1/20 = .05 P(B and C) = 3/20 = .15 P(A and C) = 4/20 = .2 To be independent P(A and B) = P(A)*P(B) and so on. The only pairs of events in whic ...
... C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A and B = (3} A and C = {2, 3, 5, 7} B and C = {3, 6, 9} P(A) = 8/20 = .4 P(B) = 6/20 = .3 P(C) = 10/20 = .5 P(A and B) = 1/20 = .05 P(B and C) = 3/20 = .15 P(A and C) = 4/20 = .2 To be independent P(A and B) = P(A)*P(B) and so on. The only pairs of events in whic ...
Chapter 2 - Brock University
... Pr(A) · Pr(B), and also to Pr(A|B) = Pr(A), meaning that A is independent of B. The same condition is also equivalent to Pr(A ∩ B) = Pr(A) · Pr(B), etc. Example: An outcome of one die cannot influence the outcome of another die; but also: an outcome of a die cannot influence any of its future outco ...
... Pr(A) · Pr(B), and also to Pr(A|B) = Pr(A), meaning that A is independent of B. The same condition is also equivalent to Pr(A ∩ B) = Pr(A) · Pr(B), etc. Example: An outcome of one die cannot influence the outcome of another die; but also: an outcome of a die cannot influence any of its future outco ...
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.