M118 SECTION 8.1 - SAMPLE SPACES, EVENTS, and PROBABILITY
... b) P(at least 1 head) = HT, TH, HH = c) P(at least 1 head or at least 1 tail) = d) P(0 heads) = EQUALLY LIKELY ASSUMPTION: Let S = a sample space with n elements. We assume each simple event ei is as likely to occur as any other, then we assign the probability 1/n to each simple event P(ei) = 1/n Ex ...
... b) P(at least 1 head) = HT, TH, HH = c) P(at least 1 head or at least 1 tail) = d) P(0 heads) = EQUALLY LIKELY ASSUMPTION: Let S = a sample space with n elements. We assume each simple event ei is as likely to occur as any other, then we assign the probability 1/n to each simple event P(ei) = 1/n Ex ...
Section 5-1
... random. What is the likelihood that all 10 favor abolishing evening exams? Describe how you could use the random digit table to simulate the 10 randomly selected students. State the problem or describe the random phenomenon: ...
... random. What is the likelihood that all 10 favor abolishing evening exams? Describe how you could use the random digit table to simulate the 10 randomly selected students. State the problem or describe the random phenomenon: ...
Document
... the probability of error The probability of getting some bit wrong is Pr[Estimate-Had(ei) is wrong for some i] ≤ ne-(ke2) Taking k = O(logn/e2) gives an O(nlogn/e2) algorithm with arbitrarily small error Note that the error probability is doubled, so doesn’t work with p<3/4 ...
... the probability of error The probability of getting some bit wrong is Pr[Estimate-Had(ei) is wrong for some i] ≤ ne-(ke2) Taking k = O(logn/e2) gives an O(nlogn/e2) algorithm with arbitrarily small error Note that the error probability is doubled, so doesn’t work with p<3/4 ...
Lecture_7 - New York University
... • Generalized Pigeonhole Principle: For any function f : X Y acting on finite sets, if n(X) > k * N(Y), then there exists some y from Y so that there are at least k + 1 distinct x’s so that f(x) = y • “If n pigeons fly into m pigeonholes, and, for some positive k, m >k*m, then at least one pigeonh ...
... • Generalized Pigeonhole Principle: For any function f : X Y acting on finite sets, if n(X) > k * N(Y), then there exists some y from Y so that there are at least k + 1 distinct x’s so that f(x) = y • “If n pigeons fly into m pigeonholes, and, for some positive k, m >k*m, then at least one pigeonh ...
Chapter 5 Notes
... Chapter 5 In Class Review Does power corrupt decision making? “Absolutely” according to an article in The Economist (January 23-29, 2010). In an experiment described by the article, a group of 15 volunteers were primed to feel powerful and then asked to roll two 10-sided dice (each having sides 0-9) ...
... Chapter 5 In Class Review Does power corrupt decision making? “Absolutely” according to an article in The Economist (January 23-29, 2010). In an experiment described by the article, a group of 15 volunteers were primed to feel powerful and then asked to roll two 10-sided dice (each having sides 0-9) ...
ch. 5 - Steve Willott`s
... Stratified Sampling: Suppose I want to choose a simple random sample of size 6 from a group of 60 boys and 30 girls. To do this, I write each person’s name on an equally sized piece of paper and mix them up in a large grocery bag. Just as I am about to select the first name, a thoughtful student sug ...
... Stratified Sampling: Suppose I want to choose a simple random sample of size 6 from a group of 60 boys and 30 girls. To do this, I write each person’s name on an equally sized piece of paper and mix them up in a large grocery bag. Just as I am about to select the first name, a thoughtful student sug ...
Algebra II Module 4, Topic A, Overview
... Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of s ...
... Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of s ...
Sample Space name
... Determine the sample space for throwing a 4 sided dice followed by tossing a nickel followed by tossing a dime. Use a probability tree. Try vertically. ...
... Determine the sample space for throwing a 4 sided dice followed by tossing a nickel followed by tossing a dime. Use a probability tree. Try vertically. ...
(i) f(x,y) - Vutube.edu.pk
... As indicated in the last lecture, using the rule of combinations in conjunction with the classical definition of probability, the probability of the first cell came out to be 3/28. By similar calculations, we obtain all the remaining probabilities, and, as such, we obtain the following bivariate ta ...
... As indicated in the last lecture, using the rule of combinations in conjunction with the classical definition of probability, the probability of the first cell came out to be 3/28. By similar calculations, we obtain all the remaining probabilities, and, as such, we obtain the following bivariate ta ...
311 review sheet. The exam covers sections 3.4, 3.5, 3.6, 3.7, 3.8
... 311 review sheet. The exam covers sections 3.4, 3.5, 3.6, 3.7, 3.8, 4.1, 4.2, 4.3, 4.4, and 4.6 from the text. Sections 4.1 and 4.2 cover general theory about continuous random variables. Otherwise the material covers some named distributions: the geometric, the negative binomial, the Poisson, the h ...
... 311 review sheet. The exam covers sections 3.4, 3.5, 3.6, 3.7, 3.8, 4.1, 4.2, 4.3, 4.4, and 4.6 from the text. Sections 4.1 and 4.2 cover general theory about continuous random variables. Otherwise the material covers some named distributions: the geometric, the negative binomial, the Poisson, the h ...
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.