Wednesday, May 22, 2019
Review of The DrunkardÃ¢â¬â¢s Walk Ã¢â¬ How Randomness Rules Our Lives by Mlodinow Essay
Read the book The Drunkards Walk How Randomness Rules Our Lives by Mlodinow and pay special attend to the fol let outing questions. Some of these questions may appear on quizzes and exams.Chapter 1 Peering through the Eyepiece of Randomness1. Explain the phenomenon r constantlyse toward the mean.In any series of ergodic events an extraordinary event is near likely to be followed, due unadulteratedly to receive, by a more ordinary unity.2. What factors de considerationine whether a person entrust be successful in c atomic number 18er, investment, etc.? Success in our careers, in our investments, and in our life decisions, both major and minoris as much the go away of random factors as the result of skill, preparedness, and hard work.3. Was Paramounts firing of Lansing the correct decision? After she was fired, Paramount films market share rebounded. No, Lansing was fired beca pulmonary tuberculosis of industrys misunderstanding of randomness and not because of her drive flawed decision making. Lansing had good luck at the beginning and bad luck at the end.Chapter 2 The Laws of Truths and Half-Truths1. What coined the term luck, or probabilis? (Latin probabilis credible) Ciceros principal legacy in the field of randomness is the term he used, probabilis, which is the origin of the term we employ to twenty-four hours. barely it is nonpareil p subterfuge of the Ro homophile code of law, the Digest, compiled by Emperor Justinian in the sixth century, that is the first document in which probability appears as an foreveryday term of art2. What is the rule for compounding probabilities? How to compute probability that one event and another event both happening? According to the correct manner of compounding probabilities, not only do both half proofs yield less than a whole certainty, but no finite number of partial proofs will ever add up to a certainty because to compound probabilities, you dontadd them you multiply. That brings us to our next law , the rule for compounding probabilities If cardinal possible events, A and B, are independent, then the probability that both A and B will occur is equal to the product of their individual probabilities.3. Is the Roman rule of half proofs two half proofs constitute a whole proof, correct? What do two half proofs constitute by the rule of compounding probabilities? 4. Suppose an airline has 1 seat left on a flight and 2 passengers have yet to show up. If there is a 2 in 3 chance a passenger who books a seat will arrive to claim it, what is the probability that the airline will have to deal with an unhappy customer? What is the probability that neither customer will show up? What is the assumption?What is the probability that either both passengers or neither passenger will show up? 5. In DNA testing for legal trial, there is 1 in 1 billion fortuityal match and 1 in 100 laberror match. What is the probability that there is both an accidental match and a lab error? What is the proba bility that one error or the other occurred? Which probability is more relevant?Chapter 3 Finding Your Way through a Space of Possibilities1. What is sample space?2. What is Cardanos law of the sample space? (P. 62)3. In the Monty H from each one problem, why should the player switch after the hosts intervention? Chapter 4 Tracking the Pathways to Success1. The grand duke of Tuscanys problem what is the probability of obtaining 10 when you ca-ca three dice? What about 9?2. What is Cardanos law of the sample space?3. What is the application of Pascals triangle?4. For the Yankees-Braves World Series example, for the rest 5 games, what is the probability that the Yankees win 2 games? 1 game?5. What is mathematical expectation?6. Explain why a state lottery is equivalent to Of all those who pay the dollar or two to enter, most will receive nothing, one person will receive a fortune, and one person will be put to death in a violent manner?Chapter 5 The Dueling Laws of Large and Small Numbers?1. What is Benfords law? Discuss about applications in business. 2. Explain the difference between the frequency interpretation and the subjective interpretation of randomness.3. Do psychics exist?4. What is tolerance of error, tolerance of uncertainty, statistical significance? 5. outline some applications from the book of the law of large numbers and the law of small numbers.Chapter 6 Bayess guess1. Two-daughter problemIn a family with two children, what are the chances that both children are girls? autonomic nervous system 25%In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? Ans 33%In a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls? Ans 50%2. How to apply Bayess Theory to determine car insurance rates? Ans Models employed to determine car insurance rates include a mathematical function describing, per unit of driving time, y our personal probability of having zero, one, or more accidents. Consider, for our purposes, a simplified model that places everyone in one of two categories high attempt, which includes drivers who mean(a) at to the lowest degree one accident each year, and low risk, which includes drivers who average less than one. If, when you apply for insurance, you have a driving record that stretches back twenty years without an accident or one that goes back twenty years with thirty-seven accidents, the insurance telephoner can be pretty sure which category to place you in.But if you are a new driver, should you be classified as low risk (a kid who obeys the speed limit and volunteers to be the designated driver) or high risk (a kid who races down Main Street swigging from a half-empty $2 bottle of Boones Farm apple wine-colored)? Since the company has no entropy on youno idea of the position of the first ballit might assign you an equal priorprobability of being in either group, or it might use what it knows about the general population of new drivers and start you off by guessing that the chances you are a high risk are, say, 1 in 3. In that case the company would model you as a hybridone-third high risk and two-thirds low riskand charge you one-third the price it charges sorry drivers plus two-thirds the price it charges low risk drivers. Then, after a year of observationthat is, after one of Bayess second balls has been thrownthe company can employ the new data send to reevaluate its model, adjust the one-third and two-third proportions it previously assigned, and recalculate what it ought to charge. If you have had no accidents, the proportion of low risk and low price it assigns you will increase if you have had two accidents, it will decrease.The precise size of the adjustment is given by Bayess theory. In the aforementioned(prenominal) manner the insurance company can periodically adjust its assessments in later years to reflect the fact that you were accident-free or that you twice had an accident date driving the wrong way down a one way street, holding a cell phone with your left hand and a ringing with your right. That is why insurance companies can give out good driver discounts the absence of accidents elevates the posterior probability that a driver belongs in a low-risk group.3. hazard of correct diagnosisSuppose in 1989, statistics from the Centers for Disease Control and Prevention show about 1 in 10,000 heterosexual non-IV-drug-abusing white male Americans who got tested were infected with HIV. Also suppose about 1 person out of every 10,000 will test positive due to the presence of the infection. Suppose 1 in 1,000 will test positive even if not infected with HIV (false positive). What is the probability that a patient who tested positive is in fact healthy?Ans So if you test 10 000 people you will have 11 positives 1 who is really infected, 10 are false positives. Of the 11 positive testees, only 1 has HIV, that is, 1/11. Therefore the probability that a positive testee is healthy = 10 / 11 = 90.9%4. O. J. Simpson trialAccording to FBI statistics, 4 million women are battered annually by husbands and boyfriends in U.S. and in 1992 1,432 or 1 in 2500 were killed by their husbands or boyfriends. The probability that a man who batters his married woman will go on to kill her is 1 in 2500. The probability that a battered wife who was murdered was murdered by her maltreater is 90%. Which probability is relevant to the O. J. trial? What is the fundamental difference between probability and statistics?Ans 1) Relevant one is the probability that a battered wife who was murdered was murdered by her abuser = 90%. 2)the fundamental difference between probability and statistics the former concerns predictions based on fixed probabilities the latter concerns the conclusion of those probabilities based on observed data.Chapter 7 Measurement and the Law of Errors1. ElectionWhy did the author argue that when elections come out extremely close, perhaps we ought to shoot them as is, or flip a coin, rather than conducting recount after recount? Ans (pg= 127 and 128) Elections, like all measurements, are imprecise, and so are the recounts, so when elections come out extremely close, perhaps we ought to accept them as is, or flip a coin, rather than conducting recount after recount.2. What is mathematical statistics?Ans numeral statistics, provides a set of tools for the interpretation of the data that arise from observation and experimentation. Statisticians sometimes view the growth of modern science as revolving around that development, the creation of a theory of measurement. But statistics also provides tools to address real-world issues, such as the effectiveness of drugs or the popularity of politicians, so a proper understanding of statistical reasoning is as useful in everyday life as it is in science.3. Wine tastingShould we believe in wine ratings from those wine experts? W hy or why not?Two groups wine tasting experts produce the following results (a) 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90(b) 80 81 82 87 89 89 90 90 90 91 91 94 97 99 100Compare the two groups of data. (pg 134)From the theoretical viewpoint, there are many reasons to question the significance of wine ratings. For one thing, taste perception depends on a complex interaction between taste and olfactory stimulation. Strictly speaking, the sense of taste comes from five types of receptor cells on the tongue salty, sweet, sour, bitter, and umami. The last responds to certain amino acid compounds (prevalent, for example, in soy sauce). But if that were all there was to taste perception, you could mimic everythingyour favorite steak, baked potato, and apple pie feast or a nice spaghetti Bologneseemploying only table salt, sugar, vinegar, quinine, and monosodium glutamate.Fortunately there is more to gluttony than that, and that is where the sense of fume comes in. The sense of smell e xplains why, if you take two identical solutions of sugar water and add to one a (sugar-free) essence of strawberry, it will taste sweeter than the other.15 The perceived taste of wine arises from the do of a stew of between 600 and 800 volatile organic compounds on both the tongue and the nose.16 Thats a problem, given that studies have shown that even flavor-trained professionals can seldom reliably identify more than three or four components in a mixture4. Can professional mutual fund managers (stock chargeers) beat students who pick stocks by tossing coins?5. What is the margin of error in a examine? Should variation within the margin of error be ignored in a poll?Ans 5% (or 3.5%). Yes, any variation within the margin of error should be ignored in a poll6. What is the central limit theorem?Ans The probability that the sum of a large number of independent random factors will take on any given value is distributed according to the conventionalismdistribution.Chapter 8 The Ord er in Chaos1. Who are the founders of statistics?Graunt and his friend William Petty have been called the founders of statistics, a field sometimes considered lowbrow by those in pure mathematics owing to its focus on mundane practical issues, and in that sense John Graunt in particular makes a fitting founder.2. How did Graunt estimate the population of London in 1662? What is Graunts legacy? From the bills of mortality, Graunt knew the number of births. Since he had a rough idea of the fertility rate, he could infer how many women were of childbearing age. That datum allowed him to guess the total number of families and, using his own observations of the mean size of a London family, thereby estimate the citys population. He came up with 384,000 previously it was believed to be 2 million.Graunts legacy was to demonstrate that inferences about a population as a whole could be made by carefully examining a limited sample of data. But though Graunt and others made valiant efforts to learn from the data through the application of simple logic, most of the datas secrets awaited the development of the tools created by Gauss, Laplace, and others in the nineteenth and early twentieth centuries.3. How did Poincare show the baker was shortchanging customers? French mathematician Jules-Henri Poincar employed Qutelets method to apprehend a baker who was shortchanging his customers. At first, Poincar, who made a habit of picking up a loaf of bread each day, noticed after deliberateness his loaves that they averaged about 950 grams instead of the 1,000 grams advertised. He complained to the authorities and afterward received bigger loaves.Still he had a hunch that something about his bread wasnt kosher. And so with the patience only a famousor at least tenuredscholar can afford, he carefully weighed his bread every day for the next year. Though his bread now averaged closer to 1,000 grams, if the baker had been honestly handing him random loaves, the number of loaves hea vier and lighter than the mean should havediminished following the bellshaped ideal of the error law. Instead, Poincar found that there were too few light loaves and a surplus of heavy ones. He concluded that the baker had not ceased baking scraggy loaves but instead was seeking to placate him by always giving him the largest loaf he had on hand.4. Are all data in night club such as financial realm normal? (Yes) Are film tax data normal? (No) For one thing, not all that happens in society, curiously in the financial realm, is governed by the normal distribution. For example, if film revenue were normally distributed, most films would earn near some average amount, and two-thirds of all film revenue would fall within a standard deviation of that number.But in the film business, 20 percent of the movies bring in 80 percent of the revenue. such(prenominal) hit-driven businesses, though thoroughly unpredictable, follow a far different distribution, one for which the concepts of mea n and standard deviation have no meaning because there is no typical executing, and megahit outliers, which in an ordinary business might occur only once every few centuries, happen every few years.5. Who dubbed the phenomenon regression toward the mean? Explain its meaning. Galton dubbed the phenomenonthat in linked measurements, if one measured quantity is far from its mean, the other will be closer to its meanregression toward the mean.6. Who coined the term the coefficient of correlation? Explain its meaning. Galton coined the term the coefficient of correlation .The coefficient of correlation is a number between 1 and 1 if it is near 1, it indicates that two variables are linearly link up a coefficient of 0 means there is no relation.7. Discuss the applications of the chi-square test?(Pg 165 166 167) Pearson invented a method, called the chi-square test, by which you can determine whether a set of data actually conforms to the distribution you believe it conforms to.8. What i s statistical physics?James Clerk Maxwell and Ludwig Boltzmann, two of the founders of statistical physics. statistical physics was aimed at explaining a phenomenon called Brownian motion. Statistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems.9. What is a drunkards walk or random walk?The random motion of molecules in a fluid can be viewed, as a metaphor for our own paths through life, and so it is worthwhile to take a little time to give Einsteins work a closer look. According to the atomic picture, the fundamental motion of water molecules is chaotic. The molecules fly first this way, then that, moving in a straight line only until deflected by an encounter with one of their sisters. As mentioned in the Prologue, this type of pathin which at various points the direction changes randomlyis often called a drunkard s walk, for reasons obvious to anyone who has ever enjoyed a few too many martinis (more sober mathematicians and scientists sometimes call it a random walk).Chapter 9 Illusions of Patterns and Patterns of Illusion1. What caused the table to move, spirit?not a direct consequence of reality but rather an act of imagination.2. What is significance testing?Significance testing, was developed in the 1920s by R. A. Fisher, one of the great statistician for scientific research. It is a formal procedure for calculating the probability of our having observed what we observed if the hypothesis we are testing is true. If the probability is low, we reject the hypothesis. If it is high, we accept it.3. Why did Apple founder Steve Jobs made the ipods shuffling feature less random to make it feel more random?Spencer-Browns point was that there is a difference between a process being random and the product of that process appearing to be random. Apple raninto that issue with the random shuffling method it initially employed in its iPod music players true randomness sometimes produces repetition, but when users heard the same song or songs by the same artist played back-to-back, they believed the shuffling wasnt random. And so the company made the feature less random to make it feel more random, give tongue to Apple founder Steve Jobs.4. Suppose there are 1000 mutual fund managers picking stock for 15 consecutive years by each tossing a coin once a year. If a head is obtained, he/she beats the market (a fund manager either beats the market average or not). What is the probability that someone among the 1000 who would toss a head in each of the 15 years? From Nobel Prize-winning economist Merton Miller If there are 10,000 people looking at the stocks and trying to pick winners, one in 10,000 is going score, by chance alone, and thats all thats going on.Its a game, its a chance operation, and people think they are doing something purposeful but theyre really not. Ans The chan ces that, after fifteen years, a particular coin tosser would have tossed all heads are then 1 in 32,768. But the chances that someone among the 1,000 who had started tossing coins in 1991 would have tossed all heads are much higher, about 3 percent.5. What is confirmation bias?When we are in the grasp of an illusionor, for that matter, whenever we have a new ideainstead of prying for ways to prove our ideas wrong, we usually attempt to prove them correct. Psychologists call this the confirmation bias, and it presents a major impediment to our ability to break free from the misinterpretation of randomness.Chapter 10 The Drunkards Walk1. What is the butterfly effect?The butterfly effect, based on the implication that atmospheric changes so small they could have been caused by a butterfly flapping its wings can have a large effect on subsequent global weather patterns. 2. Can past performance of mutual fund managers predict future performance? No.