Concept of Randomness in Statistics

Concept of Randomness in Statistics Part I Introduction Introduction on Freshman Seminar Freshman seminar 1205M offers great opportunities for students to work intimately with professors from the Science faculty on various areas of mathematics. The seminar was targeted to encourage us to open our minds to creative ideas and develop curiosity of influential mathematical theories and various subgroups of contemporary mathematics. In addition to exposure to selected subtopics in contemporary mathematics, we had valuable opportunities to develop our presentation and academic essay writing skills. 1.2 Important roles of Analogy and Intuition The historical development of mathematics is significantly influenced by intuition acquired from real life experience and analogy quoted from various other areas (Harrison Treagust, 1993). Analogy is an extraordinary method in developing new concepts in the history of science. In this module, famous topics in the contemporary mathematics, including geometry, number theory, set theory, randomness and game theory have been discussed. Among all topics, our team worked on Analogy and Intuition of Randomness. In this seminar, various creative analogy ideas and intuition/counter-intuition thinking have been presented based on specific cases in modern mathematics. 1.3 Method on Research and Presentation Our team collected relevant source materials on the randomness, including books, journals, and websites on the Internet. As for presenting applications of randomness, in particular, we focused on the historical development of randomness theory, the simplified key concepts in randomness, the counter-intuitive stories happened, overlapping with other fields in nature, and some significant and influential applications of randomness theory in our daily life. We omitted complicated theories, technical formulas and rigorous proofs. Throughout the whole semester, our team has conducted two informal presentations on randomness. In order to illustrate randomness clearly and intuitively, we adopted various methods: problem solving, in-class quizzes, presentations and attractive stories. Subtopics included: Biology, quantum physics, finance, audio engineering, statistics and so on. Part II Report on Randomness 2.1 Randomness on Communication Theory 2.1.1 Introduction of Noise in Communication Theory In statistics, irrelevant or meaningless data is considered noise (random error). Whereas in communication theory, random disturbance in a signal is called noise. In essence, noise consists of a large number of disturbances with a statistically randomized time distribution. It is assumed that noise signals have power spectral density that is proportional to 1/f^ÃŽ ², where f stands for frequencies of noise. For example, the spectral density of white noise is ÃŽ ² = 0, while pink noise has ÃŽ ² = 1. This special character is widely used for distinguishing among colors of noise. 2.1.2 Laws and Criterions Used to Distinguish Colors and Characteristics of Noise The color names for noise are derived from an analogy between the spectrum of noise and the equivalent spectrum of lights with different visible colors. For instance, if we translate the sound wave of white noise into light waves, the resulting light will be viewed as white color. In electronics, physics, and many other areas, the color of a noise signal is usually understood as some characteristics of its power spectrum. As different colors of noise have significantly different properties. Therefore, each kind of noise requires a specific color to match with it. Start with the most well-known one: White noise, people name different noise after colors. This is in analogy with white color light, which has a flat spectrum of power on its frequency range. Other colors, such as violet, blue, red, pink, are then given to different noises with extremely similar spectrum characteristics. Although most of them have standardized noise patterns with specific disciplines, there are also plenty of noise spectrums with imprecise and informal definitions, like black noise, green noise, brown noise and so on. These below parts were summarized from Wikipedia terms: Noise (electronics) Sites: http://en.wikipedia.org/wiki/Noise_%28electronics%29 2.1.3 Inner Sources of Noise Thermal noise is generated from the random thermal motion of charges (usually electrons) inside electrical conductors. The amplitude of the signal has a probability density function similar to the Gaussian (Normal) distribution. The amplitude of thermal noise depends on the temperature of the circuit. Shot noise results from unavoidable random fluctuations when the charges (such as electrons) jump over a gap inside the electric circuits. It sounds rather similar to the noise created by rain falling on a tin roof. Flicker noise has a frequency spectrum that falls down into the higher frequencies areas steadily. Burst noise consists of sudden step-like transitions between two or more levels at random and unpredictable times. It sounds like eating popcorn. 2.1.4 Outer sources of Noise Atmospheric noise is the natural disturbance caused by electricity discharges in thunderstorm and other natural disturbances occurring in nature, like disruptions of high-voltage wires. Industrial noises are produced by automobiles, aircrafts and so on. The disturbances are produced by the discharge processes in these operations as well, which is similar to the atmospheric noise. Extraterrestrial noises come from the universe. These noises include: Solar Noise, which is a radiation from the sun due to its intense nuclear reactions and the consequent high temperature, and Cosmic Noise, which are able to transmit its radiation and cosmic rays to almost everywhere. 2.1.5 Classification of Different Colors of Noise This part was adapted and summarized from an online introductory article: â€Å"White, pink, blue and violet: The colors of noise† from the Wired Magazine Science Column, Author: Duncan Geere, Date: Apr. 07, 2011 White noise White noise has a constant power distribution density on its spectrum. It is named after the white color light, which has a flatten frequency everywhere on the spectrum. The term is widely applied in many scientific and technical areas, including physics, audio engineering, telecommunications, statistical forecasting and many other areas. Specifically, White noise is used as a generator for random numbers. In addition, weather forecasting websites also use white noise to generate random digit patterns and simulate real weather.   Pink noise The power density of pink noise decreases proportionally to 1/f. In the past, the term of flicker noise sometimes refers to pink noise, but it will be more appropriate if we strictly apply it only to electronic circuits. Moreover, Pink noise is also used in analysis of meteorological data and output radiation power of some astronomical bodies. Brown noise According to the precise definition, the term Brown noise refers to a noise whose power density decreases inversely proportional to f^2. The density function can be generated from integrating white noise or via an algorithm of Brownian motion simulation. Brown noise is not named after the color brown spectrum, which is distinct from other noises. It can be used in climatology to describe climate shifts. However, within the scientific community, scientists have been arguing about its value for such purposes for a long time.   Blue noise The power density of Blue noise is proportional to frequency. Blue noise has an increasing frequency over a finite frequency range. Blue noise is similar to pink noise, but instead of a decreasing spectrum, we observe an increasing one. Sometimes it is mixed up with Violet noise in informal discussion. Violet noise Violet noise is also known as the Purple noise. The power density of Violet noise is proportional to f^2, which means it increases in quadratic form. Violet noise is like another version of Brownian noise. Moreover, as Violet noise is the result of differentiating the white noise signal density, so people also call it the â€Å"Differentiated White noise†. Grey noise Grey noise is a special kind of white noise process with characteristic equal loudness curve. However, it has a higher power density at both ends of the frequency spectrum but very little power near the center. Apparently, this is different from the standard white noise which is equal loud across its power density. However, actually this phenomenon is due to the humans hearing illusion. 2.2 Randomness on Finance 2.2.1 Brief Introduction to Efficient Market Hypothesis This part was summarized based on an online informal introductory article: â€Å"The Efficient Markets Hypothesis†, Authors: Jonathan Clarks, Tomas Jandik, Gershon Mandelker, Website: www.e-m-h.org In financial fields, the efficient-market hypothesis asserts that stock market prices will evolve with respect to to a random walk. They have the same probability distribution and independent of each other. Random walk states that stocks take a random and unpredictable path. The probability of a stocks future price going up is equal to going down. Therefore, the past movement (or trend) of a specific stock price or the overall market performance cannot be used as the basis to predict future movements. In addition, it is impossible to outperform the entire market without taking additional risk or putting extra efforts. However, EMH proves that a long-term buy-and-hold strategy is the most efficient, because long term prices will approximately reflect performance of the company very well, whereas short term movements in prices can be only described as a random walk. 2.2.2 Historical Backgrounds of Efficient Market Hypothesis This part was summarized based on an online nonprofit educational website: www.e-m-h.org and a research paper: History of the Efficient Market Hypothesis, Nov.2004, Author: Martin, Sewell, Publisher: University College London. Historically, the randomness of stock market prices was firstly modelled by a French broker, Jules Regnault, in 1863. Shortly after, a French mathematician, Louis Bachelier, developed the mathematics of Brownian motion in 1900. In 1923, the famous economist, Keynes clearly stated that investors in financial markets would be rewarded not for knowing better than other participants in the market, but rather for risk taking. After the WWII, the efficient-market hypothesis emerged as an outstanding theory in the mid-1960s. In the 1960s, Mandelbrot proposed a randomness model for stock pricing. Fama discussed about Mandelbrot’s hypothesis and concluded that the market data confirmed his model. In addition, he defined the so-called â€Å"efficient market† for the first time, in his paper â€Å"Random Walks in Stock Market Prices†. He explained how random walks in stock market significantly influence individual stock prices. Later, he introduced definitions for three forms of financial market efficiency: weak, semi-strong and strong. The term was eventually popularized when Burton Malkiel, a Professor of Economics at Princeton University, published his classic and prominent book: â€Å"A Random Walk Down Wall Street.† 2.2.3 Three Major Types of Markets: Weak, Semi-Strong and Strong The three types of EMH were summarized based on an online technical blog: â€Å"The Efficient Markets Hypothesis†, Author: Jodi Beggs, Website: About.com   Weak Form of Efficiency We cannot predict future prices through analyzing prices from the past. And we cannot earn excessive returns by using information based on historical data. In this level, technical analysis is always profitable, as share prices exhibit no dependencies on their past. This implies that future prices depend entirely on performance of companies. Semi-Strong Form of Efficiency Information other than market data is released, such as instant news, companies’ management, financial accounting reports, companies’ latest products. Under such condition, share prices will reflect the new information very rapidly. Therefore, investors cannot gain any excess returns by trading on the public information. Semi-strong-form efficiency market implies that neither technical analysis nor fundamental analysis can produce excess returns. Strong Form of Efficiency   Under such condition, information typically held by corporate insiders is released. Therefore, share prices reflect not only previously public information, but all private information as well. Theoretically, no one can earn excess returns. However, even before major changes are exposed to the public, corporate insiders are able to trade their company’s stocks from abnormal profits. Fortunately, such insider trading is banned by surveillance authorities, like the Securities and Exchange Commission. 2.2.4 Arguments and Critics on Efficiency Market Hypothesis However, critics blame that the theory’s applications in markets results in financial crisis. In response, proponents of the hypothesis state that the theory is only a simplification model of the world, which means that it may not always hold true under every conditions. Hence, the market is only practically efficient for merely investment purposes in the real world rather than other aims. 2.2.5 Interesting Counter-intuitive Stories on Monkeys   The story was adapted from the Forbes Magazine, Personal Finance Column, Author: Rick Ferri, Date: Dec, 20, 2012 In order to verify the Efficient Market Hypothesis and illustrate the theories explicitly to the public, a group of researchers conducted a monkey experiment. They randomly picked up thirty stocks from a one thousand stocks poll and then let a hundred monkeys throw darts at the stocks printing on newspaper. They kept repeating this experiment for five decades, and tracked the results. In the end, to their surprise, monkeys’ performance beat the index by 1.7% per year, which indicates that, there is certain situation where traditional technical analysis cannot even beat randomly-selected portfolios. The results have shocked the whole world by how greatly randomness affects the market stock prices. 2.3 Randomness in Physics and Biology 2.3.1 Application of Randomness in Modern Physics In the early 19th century, physicists use the philosophy of randomness to study motions and behaviors of molecules, and they build models in thermodynamics to explain phenomenon in gas experiments. In the 20th century, when the era comes for quantum mechanics, microscopic phenomena are considered as completely random. Randomness of things like radioactive decay, photons passing through polarizers, and other bizarre quantum effects cannot be explained and predicted with classical theories in the usual way (Scott, 2009). Therefore, physicists propose a new theory, which claims that in a microscopic world, some of the outcomes appear casual and random. For example, when we describe a radioactive atom, we cannot predict when the atom will decay. What only left for us is the probability of decay during a specific given period. In order to solve this mystery, Einstein postulates the Hidden Variable theory, which states that nature contains irreducible randomness: properties and variables work beyond our scope somehow, but they actually determine the outcomes appear in our world. 2.3.2 Application of Randomness in Biology The modern evolutionary states that the diversity of life is due to natural selection. Randomness, an essential component of biological diversity, is associated with the growth of biological organization during evolution (Longo Montevil, 2012). It plays important roles in determining genetic mutation, and the significance of randomness effects appear at different sizes, from microorganisms to large mammals (Bonner, 2013). During this process, a number of random genetic mutations appear in the gene library under both inner and other influences. Although this process is purely random, it indeed systematically leads to a higher chance for survival and reproduction of those individuals who possess these mutations than those without them. This mechanism plays crucial roles in the survivals of animals. Surprisingly, randomness in biology has remarkable relations to quantum physics. Schrodinger proposes his notion of negative entropy as a form of Gibbs free energy, which also behaves similarly to randomness properties in abstract quantum world (Schrodinger, 1944). Part III References Beggs, J. (2014). The Efficient Markets Hypothesis. About. Retrieved Mar 30, 2014 from http://economics.about.com/od/Financial-Markets-Category/a/The-Efficient-Markets-Hypothesis.htm Bonner, J. (2013). Randomness in Evolution. Princeton University Press. Retrieved Mar 30, 2014 from http://press.princeton.edu/titles/9958.html Clarke, J. Jandik, T. (2012). The Efficient Markets Hypothesis. Retrieved Mar 30, 2014 from http://ww.e-m-h.org/ClJM.pdf Ferri, R. (2012). Any Monkey Can Beat The Market. Forbes. Retrieved Mar 30, 2014 from http://www.forbes.com/sites/rickferri/2012/12/20/any-monkey-can-beat-the-market/ Geere, D. (2011). White, pink, blue and violet: The colors of noise. Wired. Retrieved Mar 30, 2014 from http://www.wired.co.uk/news/archive/2011-04/7/colours-of-noise/viewall Harrison, A. G., Treagust, D. F. (1994). Science analogies. The Science Teacher, 61, 40-43. Longo, G Montevil, M. (2012). Randomness Increases Order in Biological Evolution. Retrieved Mar 30, 2014 from http://www.researchgate.net/profile/Giuseppe_Longo2/publication/221350338_Randomness_Increases_Order_in_Biological_Evolution/file/60b7d51544f17cb8d8.pdf Schrodinger, E.: What Is Life? Cambridge U.P. (1944) Scoot, J. (2009). Do physicists really believe in true randomness? Ask a Mathematician. Retrieved Mar 30, 2014 from http://www.askamathematician.com/2009/12/q-do-physicists-really-believe-in-true-randomness/ Sewell, M. (2004). History of the efficient market hypothesis. Retrieved Mar 30, 2014 from http://www.cs.ucl.ac.uk/fileadmin/UCL-CS/images/Research_Student_Information/RN_11_04.pdf

Channel Distribution

HISTORY OF PROCTER & GAMBLE:Procter & Gamble Co., also known as P&G, is an American multinational consumer goods company headquartered in downtown Cincinnati, Ohio, United States. Its products include pet foods, cleaning agents, and personal care products. Prior to the sale of Pringles to the Kellogg Company, its product line included foods and beverages. In 2012, P&G recorded $83.68 billion in sales. Fortune magazine awarded P&G a top spot on its list of â€Å"Global Top Companies for Leaders†, and ranked the company at fifteenth place of the â€Å"World's Most Admired Companies† list.Chief Executive Magazine named P&G the best overall company for leadership development in its list of the â€Å"40 Best Companies for Leaders†.THE POWER OF PURPOSE:Companies like P&G are a force in the world. Our market capitalization is greater than the GDP of many countries, and we market our products in more than 180 countries. With this stature comes both responsibility and opp ortunities. Our responsibility is to be an ethical corporate citizen-but our opportunity is something far greater, and is embodied in our PURPOSE. P&G’s Purpose Statement articulates a common goal that inspires us daily:â€Å"We will provide branded products and services of superior quality and value that improves the lives of the world’s consumers, now and generations to come. As a result, consumers will reward us with leadership sales, profit, and value creation, allowing our people, our shareholders, and the communities in which we live and work to prosper.†P&G PRODUCT:Downy is a brand name of fabric softener produced by Procter & Gamble and sold in the United States. It entered the U.S. test market in August 1960 and went nationwide in December 1961. It was also sold in Philippines, Malaysia, Indonesia, Singapore, Thailand, Vietnam, Egypt and Latin America. Lenor is a brand name of fabric softener and dryer sheets, also produced by Procter & Gamble, sold in Europe, Russia, China and Japan. Plans to rebrand Lenor as Downy in the UK were dropped in 2002.CONCLUSION:My conclusion about my research about the retailers and suppliers of P&G is they have so many products manufactured inside and outside the Philippines, that’s why they are one of the best chosen products/company here in our country because of their quality and service they are providing to the customers so the customers can satisfy the needs and wants of their fellow customers. I also want to include that P&G will inspire many Filipinos to their products they introduce each and every time they produce a new product to the market.

Unusual Article Uncovers the Deceptive Practices of Funny Essay Topics

Unusual Article Uncovers the Deceptive Practices of Funny Essay Topics Pretty soon, you will be informed enough to provide a slyly humorous take. Why smart folks don't know they have the incorrect ideas. At precisely the same time, however, clearly someone might have used a tiny Journalism 101. Time is your enemy Time is likewise an important issue. What's funny to you might not be funny to your readers. You will need to provide your readers enough information so that they fully see what you're writing about. Tell our experts what kind of homework help on the internet you want to get. The help here comes in various categories. What You Should Do to Find Out About Funny Essay Topics Before You're Left Behind You could also get in touch with your writer to supply some added recommendations or request information regarding the order's progress. Creating an outline is a significant portion of writing. To be able to compose a funny text you need to decide on an intriguing t opic and after that use the perfect words. The whole procedure of applying to college is tricky from the beginning. All About Funny Essay Topics Humor is really an art that you want to master. Writing about nuclear weapons is always an excellent idea. Tattoo is a kind of art made by the qualified artists. Tattoos mean unique things to various folks. How dates differ in type and the various types. From time to time, you might be asked to compose funny texts about serious things. You've got a fantastic future ahead of you, kid even should you need a small work by means of your punctuation and grammar. You may want to include a succinct history of plastic surgery and why it has gotten so popular. Students wish to learn the skills to turn into fantastic writers but they also wish to delight in the assignment enough they are driven to work hard through each stage. 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When there's a topic which makes your blood boil, that might not be the ideal subject to write about. A wholesome dose of humor is really tough to resist. In some instances, it may include things like studying your teacher in order to know your teacher's sense of humor. Understanding Funny Essay Topics A funny essay is an essay where the writer intends to earn a reader laugh and delight in the read. however, it isn't everybody's cup of tea to compose an ideal joy ride for readers. One of the greatest hiccups in choosing funny argumentative essay topics is that comedy is a rather touchy field, and various individuals have various opinions of what comedy is about. Bear in mind that in the event that you're likely to use satire, it's also wise to utilize caution. Obviously, writing satire isn't straightforward. The Characteristics of Funny Essay Topics Bear in mind you could make funny argumentative essays if you do a few things. Not everybody can opt to write and come up with something that produces the tear gland work for the incorrect reason. If you don't know that fun is really among the costliest things on earth of today, then you truly do not know anything. Second, talk what you shouldn't do instead of what should be done. Try out another topic and do the identical 5-minute writing test till you locate a topic you know it is simple to write on. The topics must have two sides and they need to be quite intriguing. Perhaps, you should select a topic and focus on it. For instance, you can opt for a topic for elementary, middle, or higher school. Funny Essay Topics Options Why the kisses you receive from a dog are best. Papa John's swag, all which is an ideal response from the area of pizza. Bear in mind that there's no more prevalent experience than life for a member of a family. Our life is about words. All you have to do is copy the text into the text file and get started writing. 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Even in case you write about a few critical things, funny and catchy words will definitely help get to the point and create your essay simple to read. The New Angle On Funny Essay Topics Just Released Hope you get a wonderful time delivering the speech. Nobody can say he or she'd never should speech ever in its life. Evidently, at formal occasion, you've got to do speech on some selected in addition to serious issue or topic. Why free speech needs to be abolished.

Personal Pronouns in Japanese

A pronoun is a word that takes the place of a noun. In English, examples of pronouns include I, they, who, it, this, none and so on. Pronouns perform a variety of grammatical functions and are thus heavily used is most languages. There are many subtypes of pronouns such as  personal pronouns,  reflexive  pronouns,  possessive pronouns,  demonstrative pronouns, and more. Japanese vs English Pronoun Usage The use of Japanese personal pronouns is quite different from English. They are not used as often as their English counterparts, though there are a variety of pronouns in Japanese depending on the gender or the style of speech. If the context is clear, the Japanese prefer not to use the personal pronouns. It is important to learn how to use them, but also important to understand how not to use them. Unlike English, there is no strict rule to have a grammatical subject in a sentence. How to Say I Here are the different ways one can say I depending on the situation and to whom one is speaking to, whether it be a superior or a close friend. watakushi ã‚ Ã£ Å¸Ã£  Ã£ â€" --- very formalwatashi ã‚ Ã£ Å¸Ã£ â€" --- formalboku (male) Ã¥Æ'•, atashi (female) 㠁‚㠁Ÿã â€" --- informalore (male) ä ¿ º --- very informal How to Say You The following are the different ways of saying you depending on the circumstances. otaku 㠁Šã Å¸Ã£   --- very formalanata 㠁‚㠁 ªÃ£ Å¸ --- formalkimi (male) Ã¥ â€º --- informalomae (male) 㠁Šå‰ , anta 㠁‚ん㠁Ÿ--- very informal Japanese Personal Pronoun Usage Among these pronouns, watashi and anata are the most common. However, as mentioned above, they are often omitted in conversation. When addressing your superior, anata is not appropriate and should be avoided. Use the persons name instead. Anata is also used by wives when they address their husbands. Omae is sometimes used by husbands when addressing their wives, though it sounds a little bit old-fashioned. Third Person Pronouns The pronouns for the third person are kare (he) or kanojo (she). Rather than using these words, it is preferred to use the persons name or describe them as ano hito (that person). It is not necessary to include gender. Here are some sentence examples: Kyou Jon ni aimashita.ä »Å Ã¦â€" ¥Ã£â€š ¸Ã£Æ' §Ã£Æ' ³Ã£  «Ã¤ ¼Å¡Ã£ â€žÃ£  ¾Ã£ â€"㠁Ÿã€‚I saw him (John) today.Ano hito o shitte imasu ka.㠁‚㠁 ®Ã¤ º ºÃ£â€šâ€™Ã§Å¸ ¥Ã£  £Ã£  ¦Ã£ â€žÃ£  ¾Ã£ â„¢Ã£ â€¹Do you know her? Additionally, kare or kanojo often means a boyfriend or a girlfriend. Here are the terms used in a sentence: Kare ga imasu ka.Ã¥ ½ ¼Ã£ Å'㠁„㠁 ¾Ã£ â„¢Ã£ â€¹Do you have a boyfriend?Watashi no kanojo wa kangofu desu.ç § Ã£  ®Ã¥ ½ ¼Ã¥ ¥ ³Ã£  ¯Ã§Å"‹è ­ ·Ã¥ © ¦Ã£  §Ã£ â„¢My girlfriend is a nurse. Plural Personal Pronouns To make plurals, a suffix ~ tachi (é â€) is added like watashi-tachi (we) or anata-tachi (you plural). The suffix ~ tachi can be added to not only pronouns but to some other nouns referring to people. For example, kodomo-tachi (Ã¥ ­ Ã¤ ¾â€ºÃ© â€) means children. For the word anata, the suffix ~ gata (æâ€" ¹) is used sometimes to make it plural instead of using ~ tachi. Anata-gata (㠁‚㠁 ªÃ£ Å¸Ã¦â€" ¹) is more formal than anata-tachi. The suffix ~ ra (ら) is also used for kare, such as karera (they).