...Birthday Problem Subject: Mathematics Name：Dmitry Kozyrev Passport Number：N07797989 Date: 16.06.2015 Mark: Contents Abstract _______________________________________________ 3 Keywords______________________________________________ 3 1. Basis of Probability ___________________________________ 4 1.1 Conditional Probability _____________________________ 4 1.2 Independence _____________________________________ 4 2. Birthday Problem______________________________________5 2.1 What is Birthday Problem? _________________________ 5 2.2 Understanding the probability_________________________ 6 2.3 Calculating the probability of birthday problem___________ 7 2.4 Abstract proof______________________________________10 3 Examples______________________________________________11 4 References_____________________________________________13 2 Abstract The subject of probability can be traced back to the 17th century when it arose out of the study of gambling games. As we see, the range of applications extends beyond games into business decisions, insurance, law, medical tests, and the social sciences. The stock market, “the largest casino in the world,” cannot do without it. The telephone network, call centers, and airline companies with their randomly fluctuating loads could not have been economically designed without probability theory. To quote Pierre-Simon, marquis de Laplace from several hundred years ago: «It is remarkable that this science, which originated...
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...Generalization: A generalization of this problem as well as its preceding problem (When is Cheryl’s Birthday) would be to connect these questions to the ideas of the birthday paradox, and an even bigger idea of the pigeonhole principle. In math, the pigeonhole principle states that if there are n items to be put into m containers, with the criteria that n > m, then at least one container will hold more than one item. (Herstein, 1964) Another way to explain this principle in a more quantitative way would be to say that for natural numbers k and m, if n = km + 1 objects are distributed among m sets, then the pigeonhole principle asserts that at least one of the sets will contain at least k + 1 objects. (Youtube) This pigeonhole principle can...
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...3GPP-MAC beyond the Birthday Bound Liting Zhang2 , Wenling Wu1 , Han Sui2 , and Peng Wang2 Institute of Software, Chinese Academy of Sciences State Key Laboratory of Information Security Institute of Information Engineering, Chinese Academy of Sciences {zhangliting,wwl,suihan}@is.iscas.ac.cn, wp@is.ac.cn 1 2 Abstract. Among various cryptographic schemes, CBC-based MACs belong to the few ones most widely used in practice. Such MACs iterate a blockcipher EK in the so called Cipher-Block-Chaining way, i.e. Ci = EK (Mi ⊕ Ci−1 ) , offering high efficiency in practical applications. In the paper, we propose a new deterministic variant of CBC-based MACs that is provably secure beyond the birthday bound. The new MAC 3kf9 is obtained by combining f 9 (3GPP-MAC) and EMAC sharing the same internal structure, and so it is almost as efficient as the original CBC 3 3 q lq MAC. 3kf9 offers O( l22n + 2n ) PRF-security when its underlying n-bit blockcipher is pseudorandom with three independent keys. This makes it more secure than traditional CBC-based MACs, especially when they are applied with lightweight blockciphers. Therefore, 3kf9 is expected to be a possible candidate MAC in resource-restricted environments. Keywords: MAC, Birthday Bound, CBC, Mode of Operation. 1 1.1 Introduction Background Birthday Bound. In cryptography, birthday attack is a generic attack that exploits no specific properties within cryptographic schemes, but just takes the advantage of birthday paradox in probability...
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...700+ GMAT Problem Solving Probability and Combinations Questions With Explanations Collected by Bunuel Solutions by Bunuel gmatclub.com 1. Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? A. 24/64 B. 32/64 C. 36/64 D. 40/64 E. 42/64 Expected value of a roll of one dice is 1/6(1+2+3+4+5+6)=3.5. Expected value of three dices is 3*3.5=10.5. Mary scored 10 so the probability to have more then 10, or more then average is the same as to have less than average=1/2. P=1/2. Answer: B. Discussed at: http://gmatclub.com/forum/mother-mary-comes-to-me-86407.html 2. Denise is trying to open a safe whose combination she does not know. IF the safe has 4000 possible combinations, and she can try 75 different possibilities, what is the probability that she does not pick the one correct combination. A. 1 B. 159/160 C. 157/160 D. 3/160 E. 0 When trying the first time the probability Denise doesn't pick the correct combination=3999/4000 Second time, as the total number of possible combinations reduced by one, not picking the right one would be 3998/3999. Third time 3997/3998 ... And the same 75 times. So we get: [pic] every denominator but the first will cancel out and every nominator but the last will cancel out as well. We'll get 3925/4000=157/160. Answer: C. Discussed at: http://gmatclub.com/forum/4000-possible-combination-84435...
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...STAT 225: Introduction to Probability Models Extra Examples 1 Introduction to Probability Extra 1.1 Let A be an event that happens 40% of the time. Let B be an event that happens 75% of the time. Answer the following 4 questions. What is the smallest probability the intersection of A and B can have? What is the largest probability the intersection of A and B can have? What is the smallest probability the union of A and B can have? What is the largest probability the union of A and B can have? .15, .4, .75, and 1 respectively. Extra 1.2 Suppose we are rolling 2 independent, fair 10-sided die. Let A be the event that the sum of the rolls is a prime number. Let B be the event that the sum of the rolls is odd. Let C be the event that the sum of the rolls is even. Find the following sets: BC , A ∩ B, A ∪ C, A ∩ C, (A ∩ C)C , A ∩ (B ∩ C)C , (A ∩ (B ∩ C))C ? BC = C, A ∩ B = A \ {2}, A ∪ C = Ω \ {9, 15}, A ∩ C = {2}, (A ∩ C)C =Ω \ {2}, A ∩ (B ∩ C)C = A, and (A ∩ (B ∩ C))C = Ω. Extra 1.3 Suppose a lottery has balls numbered 1-20. 4 balls are picked at random and without replacement. Let A be the event that all 4 balls are even. Let B be the event that all 4 balls are less than 10. Let C be the event that all 4 balls are primes. (Allow 1 to be a prime.) Find P(A), P(B), and P(C). (Hint an extended general multiplication rule could be helpful.) P(all 4 even) = (10)4 (20)4 = .0433. (9) P(all less than 10) = (20)44 = .0260. What numbers are prime? 1, 2, 3, 5, 7, 11, 13, 17, and...
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...metaethics, which studies philosophical questions about the meaning of ethical words, or the nature of ethical facts 2. Applied ethics is a distinct category of ethical philosophy A. What is applied ethics? 3. Deals with difficult moral questions and controversial moral issues that people actually face in their lives Examples: the moral issues regarding… abortion euthanasia giving to the poor sex before marriage the death penalty gay/lesbian marriage (or other rights) war tactics censorship so-called “white lies” etc. A. What is applied ethics? 4. Given the time we have left in the semester, we’re going to focus on only two example issues: • Whether or not we are morally obligated to help the less fortunate (especially those in other nations) • Whether or not abortion is morally wrong 5. Why we haven’t spent more time on this: • Often results in gridlocked or endless discussions • Having some prior knowledge of some normative theories helps give a framework for discussion • Brings in issues that are not philosophical E.g., a discussion about whether or not the death penalty is morally OK may require sociological information about its effectiveness, etc. B. Suggestions for having good discussions 1. Abortion is a very emotional and charged issue - Students are bound to have strong, conflicting opinions. - Many students may have been personally affected. 2. To avoid a shouting match, it’s best to try to respect everyone’s opinion. 3. Focus on the arguments and not the people...
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...TeA M YYe PG Digitally signed by TeAM YYePG DN: cn=TeAM YYePG, c=US, o=TeAM YYePG, ou=TeAM YYePG, email=yyepg@msn .com Reason: I attest to the accuracy and integrity of this document Date: 2005.07.04 23:45:43 +08'00' ������������ Want to learn more? We hope you enjoy this McGraw-Hill eBook! If you’d like more information about this book, its author, or related books and websites, please click here. HOW TO ACE THE BRAINTEASER INTERVIEW JOHN KADOR M C G R AW- H I L L N E W YO R K MADRID C H I C AG O SAN FRANCISCO MILAN SYDNEY LISBON TO RO N TO LONDON S A N J UA N MEXICO CITY SEOUL NEW DELHI SINGAPORE Copyright © 2005 by John Kador. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-144606-0 The material in this eBook also appears in the print version of this title: 0-07-144001-1. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special...
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... Excel sheet: Student Name: Shaheen Sardar Department: Industrial and Management Engineering, Hanyang University, South Korea. Home Work 1 Chapter 1: Introduction to Supply Chain Management Problem 1: Consider the supply chain for a domestic automobile. a. What are the components of the supply chain for the automobile? b. What are the different firms involved in the supply chain? c. What are the objectives of these firms? d. Provide examples of conflicting objectives in this supply chain. e. What are the risks that rare or unexpected events pose to this supply chain? Answer: a. The supply chain for a car typically includes the following components:: 1. Suppliers for raw materials 2. Suppliers for parts and subsystems 3. Automobile manufacturer (Ford, in the example). Within a company, there are also different departments, which constitute the internal supply chain: i. Purchasing and material handling ii. Manufacturing iii. Marketing, etc. 4. Transportation providers 5. Automobile dealers b. Many firms are involved in the supply chain. 6. Raw material suppliers. For instance, suppliers for steel, rubber, plastics, etc. 7. Parts suppliers. For instance, suppliers for engines, steering wheels, seats, and electronic components, etc. 8. Automobile manufacturer. For instance, Ford. 9. Transportation providers...
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...cellular telecom network .Since the technology is fully digital it enables Digital encryption, which provides a moderate security of Phone conversations, compression of data, and mobile data services (eg. SMS). Today, GSM holds a share of 82.4%, includes the 3GSM service, of world mobile connection with more than 690 mobile networks spreading across 213 countries. Being the most popular mobile phone standard, GSM facilitates the network operators to have roaming agreements with other operators, even foreign operators, allowing the users continue using their mobile phones even when they travel to other countries. The Multiple access method, allowing several cells to share the same communication channel, in GSM is a variation of Time Division Multiple access(TDMA).In TDMA several users share the same frequency spectrum by establishing h links in different time slots one after the other where each user using his own time slot. By multiplexing the time space GSM supports one transmitter/receiver for several receivers/transmitters. The analogy provided by Qualcomm illustrates the concept Imagine a room full of people, all trying to carry on one-on-one conversations. In TDMA each couple takes turns talking. They keep their turns short by saying only one...
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...Consumer Behavior Assignment 1 Activity | Community | Observations | | | | | | | | | | | | | | | | | | | | | | * Marketing Manipulation : Market manipulation describes a deliberate attempt to interfere with the free and fair operation of the market and create artificial, false or misleading appearances with respect to the price of, or market for, a security, commodity or currency.[1] Market manipulation is prohibited in the United States under Section 9(a)(2)[2] of the Securities Exchange Act of 1934, and in Australia under Section s 1041A of the Corporations Act 2001. The Act defines market manipulation as transactions which create an artificial price or maintain an artificial price for a tradeable security. * Hobby -> product * Perception = view, opinion, taste, feeling, sound(hearing), touching, smell -> Sensory Stimulation Smell – Nose Touch – Skin See – eyes Sound – ears Tastes – Mouth * Expose to products -> attention -> Interpretation * Associating with sensory stimuli * Percepting * 1. Sensory Marketing Sample of perfumes [ Smell ] Music (in Zara – club music) [ Sound ] * Subliminal Messaging : Subliminal stimuli (pronounced /sʌbˈlɪmɨnəl/, literally "below threshold"), contrary to supraliminal stimuli or "above threshold", are any sensory stimuli below an individual's absolute threshold for conscious perception. Visual stimuli may be quickly flashed before an individual...
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...The Ethics Thing: Why It Matters More in Hard Times and Why It’s So Hard to Do What Makes Good and Smart People Do Dumb and Unethical Things? Professor Marianne M. Jennings W.P. Carey School of Business Ethical Lapses • • • • • • • • • • • • • • • • • • • • • • Student loan lenders: Sallie Mae and 17 universities Adelphia Boeing Cendant Computer Associates Tyco International T I t ti l General Electric Global Crossing Merrill Lynch Enron Qwest WorldCom Royal Shell Nortel Krispy Kreme Refco UnitedHealth Group Merck Chiquita World Bank BP Madoff Investment Securities • • • • • • • • • • • • • • • • • • • • • • • • • • • AT&T Titan Xerox Kmart Citigroup Lucent ImClone Arthur Andersen HealthSouth Royal Ahold Parmalat Apollo Group Marsh & McLennan AIG (twice)(Putnam)(Mercer) Fannie Mae (twice) KPMG (twice) GM Options scandals (200 companies) HP Universities and travel Siemens Countrywide Financial Société General Milberg Weiss Bear Stearns Satyam (India) Stanford Investments Jennings 1 Government Issues • • • • • • • • • • • • • • • • • • • • • • • • • • • • Illinois – Gov. Ryan Illinois – Blago Baltimore’s mayor Detroit’s mayor – Kwame Kilpatrick San Diego -- $1.1 billion pension fund deficit; skimming to meet city budget Connecticut – Gov. Rowland Chicago – Mayor’s office and contracts Embezzlement – BLM E b l t Former Delay aides and guilty pleas Abramoff Duke Cunningham -- $2.4 million from defense contractors State crime labs and scandals Tom DeLay Clark...
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... : A Batch Roll No. : P14141 | | Brainstorming: Aid to creativity | Contents: 1. Abstract ……………………………………………………………. 2 2. Introduction ………………………………………………………...3 3. Terms and concepts ………………………………………………..4 4. Brainstorming as an aid to creativity …………………………….4 5. Individual and group brainstorming ……………………………..5 6. Challenges to effective brainstorming …………………………....6 7. Advantages of group brainstorming in an organization ………...7 8. Disadvantages of group brainstorming in an organization ……..8 9. Why organizations still use brainstorming in spite of its drawbacks ………………………………………………………….....8 10. Should an organization use brainstorming? ……………………9 11. Conclusions ……………………………………………………....10 12. References ………………………………………………………..11 Abstract: In an organization, knowledge or idea exchange is an important function of groups in solving problems. Under the right conditions, the idea exchange process in groups may be an important means for enhancing creativity and innovation in organizations Creativity will help to solve a wide range of management problems. Brainstorming is use for creativity and amassing of ideas from the group. It is found that the idea sharing in groups can be productive in getting things done. Research has found that significantly fewer ideas were produced by groups than by individuals. In spite of its shortcoming organization use brainstorming for developing...
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...Introduction to the field of organizational behaviour Reflection : Even after working in Information Technology MNC's for almost four years, I never realised that organizational behaviour plays such a pivotal role in the survival of an organization and its employees. I got to know about how both the entities: organization and employee are interdependent and their survival depends on an important factor called Organizational Behaviour. I understood that to get a bird's eye view about any organization, first I need to understand about the organizational behaviour. Organization is a complex open system that depends on external environment for effective functioning. I believe that the intellectual capital is definitely a valuable asset and its sharing can be a growth factor for organization. For an effective management, we need to go through planning, organizing, leading and controlling aspects of a job in hand. Management and leadership must be important traits for a manager to enable team and organization to achieve more than just task completion. I need to develop soft skills and hard skills in a proper ratio i.e. conceptual, human and technical skills to be an effective manager in future. Also learnt how important are values and ethics to an organization and about its responsibility towards the society (CSR). Understood the fact that more globalization and increasing workforce diversity has changed the structure of corporate world and information technology has impacted the way...
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...supply chain for a car typically includes the following components: 1. Suppliers for raw materials 2. Suppliers for parts and subsystems 3. Automobile manufacturer (Ford, in this example). Within a company, there are also different departments, which constitute the internal supply chain: i. Purchasing and material handing ii. Manufacturing iii. Marketing, etc. 4. Transportation providers 5. Automobile dealers b. Many Þrms are involved in the supply chain. 1. Raw material suppliers. For instance, suppliers for steel, rubber, plastics, etc. 2. Parts suppliers. For instance, suppliers for engines, steering wheels, seats, and electronic components, etc. 3. Automobile manufacturer. For instance, Ford. 4. Transportation providers. For instance, shippers, trucking companies, railroads, etc. 5. Automobile dealers. For example, Hayward Ford. c. All companies involved in the supply chain want to maximize their respective proÞts by increasing revenue and decreasing cost. However, companies may employ different 2 strategies in order to achieve this goal. Some of them focus on customer satisfaction and quick delivery, while others may be more concerned about minimizing inventory holding costs. d. In general, different parts of the supply chain have objectives that are not aligned with each other. 1. Purchasing: Stable order quantities, ßexible delivery lead times and little variation in mix. 2. Manufacturing: Long...
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...Introduction to Supply Chain Management Discussion Questions Question 1 Pick any car model manufactured by a domestic auto maker. For example, consider the 2002 Ford Thunderbird. a. The supply chain for a car typically includes the following components: 1. Suppliers for raw materials 2. Suppliers for parts and subsystems 3. Automobile manufacturer (Ford, in this example). Within a company, there are also different departments, which constitute the internal supply chain: i. Purchasing and material handing ii. Manufacturing iii. Marketing, etc. 4. Transportation providers 5. Automobile dealers b. Many Þrms are involved in the supply chain. 1. Raw material suppliers. For instance, suppliers for steel, rubber, plastics, etc. 2. Parts suppliers. For instance, suppliers for engines, steering wheels, seats, and electronic components, etc. 3. Automobile manufacturer. For instance, Ford. 4. Transportation providers. For instance, shippers, trucking companies, railroads, etc. 5. Automobile dealers. For example, Hayward Ford. c. All companies involved in the supply chain want to maximize their respective proÞts by increasing revenue and decreasing cost. However, companies may employ different 2 strategies in order to achieve this goal. Some of them focus on customer satisfaction and quick delivery, while others may be more concerned about minimizing inventory holding costs. d. In general, different parts of the supply chain have objectives that are not aligned with each...
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