7 Domain - Hillsdale Public Schools
... satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the ...
... satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the ...
Probability Basic Concepts of Probability
... nce is m· n. This rule can be extended for any number of eve nts occurring in a sequence. ...
... nce is m· n. This rule can be extended for any number of eve nts occurring in a sequence. ...
Chapter 3: Probability
... probability of an event approaches the theoretical (actual) probability of the event. Example: ...
... probability of an event approaches the theoretical (actual) probability of the event. Example: ...
lfstat3e_ppt_03_rev
... probability of an event approaches the theoretical (actual) probability of the event. Example: ...
... probability of an event approaches the theoretical (actual) probability of the event. Example: ...
Document
... 5) Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) = P(A)P(B) This is the multiplication rule for independent events. Two consecutive coin tosses: P(first Tail and second Tail) = P(first Tail) ...
... 5) Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) = P(A)P(B) This is the multiplication rule for independent events. Two consecutive coin tosses: P(first Tail and second Tail) = P(first Tail) ...
document
... 5) Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) = P(A)P(B) This is the multiplication rule for independent events. Two consecutive coin tosses: P(first Tail and second Tail) = P(first Tail) ...
... 5) Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) = P(A)P(B) This is the multiplication rule for independent events. Two consecutive coin tosses: P(first Tail and second Tail) = P(first Tail) ...
Distributions, Histograms and Densities: Continuous Probability
... Distributions, Histograms and Densities: Continuous Probability – p.10/24 ...
... Distributions, Histograms and Densities: Continuous Probability – p.10/24 ...
Conditional Probability and Independence
... Given n events of E1 , . . . , En in a sample space S, we have P(E1 E2 · · · En ) = P(E1 )P(E2 |E1 )P(E3 |E1 E2 ) · · · P(En |E1 · · · En−1 ). ...
... Given n events of E1 , . . . , En in a sample space S, we have P(E1 E2 · · · En ) = P(E1 )P(E2 |E1 )P(E3 |E1 E2 ) · · · P(En |E1 · · · En−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.