Overview of Unit 1
... How many different sums of money can be made from the bills in (a) as well as one more $10-bill? ...
... How many different sums of money can be made from the bills in (a) as well as one more $10-bill? ...
Declarations of Independence
... with respect to another set B … is defined of course by P(A|B) = P(A ∩ B)/P(B), unless P(B) vanishes, in which case it is not defined at all” (427). Three things leap out at us here: the ratio is regarded as a definition of conditional probability; its being so regarded is obvious (“of course”); and ...
... with respect to another set B … is defined of course by P(A|B) = P(A ∩ B)/P(B), unless P(B) vanishes, in which case it is not defined at all” (427). Three things leap out at us here: the ratio is regarded as a definition of conditional probability; its being so regarded is obvious (“of course”); and ...
Lecture 2 - Probability theory
... The value of G: Frequentist interpretation (1) The frequentist’s interpretation of the statement “G = 6.6742 ± 0.0010 (standard error)” is roughly the following: The many different measurements of G performed by laboratories around the world, as well as NIST’s compilation and critical evaluation of ...
... The value of G: Frequentist interpretation (1) The frequentist’s interpretation of the statement “G = 6.6742 ± 0.0010 (standard error)” is roughly the following: The many different measurements of G performed by laboratories around the world, as well as NIST’s compilation and critical evaluation of ...
Probability Quick Review of Probability Basic Probability Rules
... A standard 6-sided die has six sides numbered 1, 2, 3, 4, 5, and 6. Each number is equally likely to be rolled (assuming a fair die). Example (Yahtzee Probability) In the game of Yahtzee, 5 six-sided dice are rolled. If all 5 dice have the same number, the roll is called a Yahtzee. What is the proba ...
... A standard 6-sided die has six sides numbered 1, 2, 3, 4, 5, and 6. Each number is equally likely to be rolled (assuming a fair die). Example (Yahtzee Probability) In the game of Yahtzee, 5 six-sided dice are rolled. If all 5 dice have the same number, the roll is called a Yahtzee. What is the proba ...
Chap2 - NCSU Statistics
... all points inside either circle (or both). The key word for expressing the union of two sets is or (meaning A or B or both). The intersection of A and B, denoted by A n B or by A B, is the set of all points in both A and B. The Venn diagram of Figure 2.4 shows two sets A and B, with A n B consisting ...
... all points inside either circle (or both). The key word for expressing the union of two sets is or (meaning A or B or both). The intersection of A and B, denoted by A n B or by A B, is the set of all points in both A and B. The Venn diagram of Figure 2.4 shows two sets A and B, with A n B consisting ...
6.4Bayesian Classification
... other classifiers that do not explicitly use Bayes’ theorem. For example, under certain assumptions, it can be shown that many neural network and curve-fitting algorithms output the maximum posteriori hypothesis, as does the naïve Bayesian classifier. Example 6.4 Predicting a class label using naïve ...
... other classifiers that do not explicitly use Bayes’ theorem. For example, under certain assumptions, it can be shown that many neural network and curve-fitting algorithms output the maximum posteriori hypothesis, as does the naïve Bayesian classifier. Example 6.4 Predicting a class label using naïve ...
Presentation Thursday March 28
... (b). What is the appropriate value for C such that a randomly chosen bolt has a width less than C with probability .8531? ...
... (b). What is the appropriate value for C such that a randomly chosen bolt has a width less than C with probability .8531? ...
We have not yet shown the necessity for σ
... 4. N ON - MEASURABLE SETS We have not yet shown the necessity for σ-fields. Restrict attention to ([0, 1], F , m) where F is either (i) B , the Borel σ-algebra or (ii) B the possibly larger σ-algebra of Lebesgue measurable sets (as defined by Caratheodary). This consists of two distinct issues. (1) ...
... 4. N ON - MEASURABLE SETS We have not yet shown the necessity for σ-fields. Restrict attention to ([0, 1], F , m) where F is either (i) B , the Borel σ-algebra or (ii) B the possibly larger σ-algebra of Lebesgue measurable sets (as defined by Caratheodary). This consists of two distinct issues. (1) ...
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.