HW 3 Solutions - Duke Computer Science
... put between the two sublists, so it is never compared with any other elements after that round is finished. c) Take the expectation of both sides of the equation in part b. By linearity expectation we have E[X] = ...
... put between the two sublists, so it is never compared with any other elements after that round is finished. c) Take the expectation of both sides of the equation in part b. By linearity expectation we have E[X] = ...
12.5 Probability of Independent & Dependent Events
... – I draw two, three, four or more cards. – I throw the die two, three, four, or more times – I draw two, three, four, or more marbles from a bag ...
... – I draw two, three, four or more cards. – I throw the die two, three, four, or more times – I draw two, three, four, or more marbles from a bag ...
Probability Concepts Probability Distributions
... How do we teach probability distributions? With lots of experiments. Almost always the questions are given in a practical situation For Poisson we had scoops of hokey pokey ice-cream and counted the lumps of hokey pokey For Binomial we used different types of dice For expected value and variance we ...
... How do we teach probability distributions? With lots of experiments. Almost always the questions are given in a practical situation For Poisson we had scoops of hokey pokey ice-cream and counted the lumps of hokey pokey For Binomial we used different types of dice For expected value and variance we ...
4th 9 weeks
... S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). ...
... S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). ...
portable document (.pdf) format
... curve fitting. There is a great body of literature on the subject, worthy of mention of which are the books by Siegel and Castellan, [1], and Sprent [2]. This paper is concerned with the computational aspects of an important distributionfree runs test, namely, the longest of runs test of randomness ...
... curve fitting. There is a great body of literature on the subject, worthy of mention of which are the books by Siegel and Castellan, [1], and Sprent [2]. This paper is concerned with the computational aspects of an important distributionfree runs test, namely, the longest of runs test of randomness ...
Example
... Examples of Random Variables Z = outcome of tossing a coin (0 for tail, 1 for head) X=number of refrigerators sold a day X=number of tokens out for a token you put into a slot machine Y=Net profit of a store in a month Table 2.5 and 2.6, p.33 ...
... Examples of Random Variables Z = outcome of tossing a coin (0 for tail, 1 for head) X=number of refrigerators sold a day X=number of tokens out for a token you put into a slot machine Y=Net profit of a store in a month Table 2.5 and 2.6, p.33 ...
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.