Suppose we take a random sample of size 100 from a discrete distribution in this manner: A green die and a red die are thrown simultaneously 100 times and... let Xi denote the sum of the spots on the two dice on the ith throw, i = 1, 2,...100. Find the probability that the sample mean number of spots on the two dice is less than 7.5. n = 100 µ = 7 µ[pic] = 7 σ = 2.41 σ[pic] = 2.41 /[pic] |X |2 |3 |4 ...
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EXERCISES (Discrete Probability Distribution) EXERCISES (Discrete Probability Distribution) P X x n C x p 1... p x BINOMIAL DISTRIBUTION n x P X x n C x p 1 p x BINOMIAL DISTRIBUTION n x 1. 2. 3. The probability that a certain kind of component will survive a given shock test is ¾. Find the probability that exactly 2 of the next 4 components tested survive. The probability that a log-on to the network is successful is 0.87. Ten users...
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is the probability that both outcomes are heads? Explain. Ans. P(H) = 1/2 Probability of 2 heads = 1/2 x 1/2... = 1/4 Q.2 Suppose that 25% of the population in a given area is exposed to a television commercial on Ford automobiles, and 34% is exposed to Ford’s radio advertisements. Also, it is known that 10 % of the population is exposed to both means of advertising. If a person is randomly chose out of the entire population on this area, what is the probability that he...
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Probability distribution Definition with example: The total set of all the probabilities of a random variable to attain all... the possible values. Let me give an example. We toss a coin 3 times and try to find what the probability of obtaining head is? Here the event of getting head is known as the random variable. Now what are the possible values of the random variable, i.e. what is the possible number of times that head might occur? It is 0 (head never occurs), 1 (head occurs once out of 2 tosses)...
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Concept and basics of probability sampling methods One of the most important issues in researches is selecting an appropriate sample. Among... sampling methods, probability sample are of much importance since most statistical tests fit on to this type of sampling method. Representativeness and generalize-ability will be achieved well with probable samples from a population, although the matter of low feasibility of a probable sampling method or high cost, don’t allow us to use it and shift us to the...
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Ans.1: Non-Probability Sampling: When the units of a sample are chosen so that each unit in the population does not have a calculable... non-zero probability of being selected in the sample, this is called Non-Probability Sampling. Also, Non-probability sampling is a sampling technique where the samples are gathered in a process that does not give all the individuals in the population equal chances of being selected. In contrast with probability sampling, non-probability sample is not a product...
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Mathematical Systems Probability Solutions by Bracket A First Course in Probability Chapter 4—Problems 4. Five men and 5... women are ranked according to their scores on an examination. Assume that no two scores are alike and all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a woman (for instance, X = 1 if the top-ranked person is female). Find P X = i , i = 1, 2, 3, . . . , 8, 9, 10. Let Ei be the event that the the ith scorer is female. Then the...
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Homework 3 Probability 1. As part of a Pick Your Prize promotion, a store invited customers to choose which of three prizes they’d like... to win. They also kept track of respondents’ gender. The following contingency table shows the results: | MP3 Player | Camera | Bike | Total | Men | 62 | 117 | 60 | 239 | Woman | 101 | 130 | 30 | 261 | Total | 163 | 247 | 90 | 500 | What is the probability that: a. a randomly selected customer would pick the camera? 247/500= 0.494=...
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Introduction Objectives PROBABILITY 2.2 Some Elementary Theorems 2.3 General Addition Rule 2.4 Conditional... Probability and Independence 2.4.1 Conditional Probability 2.4.2 Independent Events and MultiplicationRule 2.4.3 Theorem of Total Probability and Bayes Theorem 2.5 Summary 2.1 INTRODUCTION You have already learnt about probability axioms and ways to evaluate probability of events in some simple cases. In this unit, we discuss ways to evaluate the probability of combination of events...
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Bayes' theorem describes the relationships that exist within an array of simple and conditional probabilities. For example:... Suppose there is a certain disease randomly found in one-half of one percent (.005) of the general population. A certain clinical blood test is 99 percent (.99) effective in detecting the presence of this disease; that is, it will yield an accurate positive result in 99 percent of the cases where the disease is actually present. But it also yields false-positive results in 5...
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PROBABILITY QUESTIONS Q1). You draw a card at random from a standard deck of 52 cards. Neither you nor anyone else looked at the card you... picked. You keep it face down. Your friend then picks a card at random from a remaining 51 cards. a) What is the probability that your card is ace of spades? 1/52 b) What is the probability that your friend’s card is ace of spades? (Hint: Construct the sample space for what your friend’s card can be.) 1/51 c) You turn over your card and it is 10 of...
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CONDITIONAL TENSE Conditional sentences usually are of the type in which one circumstance will be symbiotic with the other.... For example, “if I find her address, I’ll send her the invite.” Normally, there are three kinds of relationships which can be expressed using the conditional- factual, future, and imaginative conditional relationship. Factual conditionals generate two branches- timeless and time-bound conditionals. Furthermore, timeless conditionals are divided into habitual and generic...
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Question 1 With the use of Merton Model, the probability of Default (PD) of each firm is summarized as follow: Company Name | ASX Code |... Probability of Default | Adelaide Brighton Limited | ABC | 0% | Buderim Ginger Limited | BUG | 26.079% | FFI Holdings Limited | FFI | 0.056% | McPherson’s Limited | MCP | 0.003% | Reece Australia Limited | REH | 0% | Vietnam Industrial Investments Limited | VII | 2.472% | Question 2 Using 15 Sep 2008 as a cut-off point, the pre and post results...
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entire populace like weight, gender, color, religion, job types, etc. Sample Data surveying is also extremely cost effective opposed to surveying an entire... population. In short, this form of Sample Data is, from my own opinion, nothing more than probability theories. Population Data On the other hand, Population Data is just that; a means or census aimed at providing Data specifically based on the demographics, collective distinctiveness of a populace, individualism, and the primary starting point...
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new Household appliance to potential customers. She has found from her years of experience that after demonstration, the probability of... purchase (long run average) is 0.30. To perform satisfactory on the job, the salesperson needs at least four orders this week. If she performs 15 demonstrations this week, what is the probability of her being satisfactory? What is the probability of between 4 and 8 (inclusive) orders? Solution p=0.30 q=0.70 n=15 k=4 [pic] Using Megastat we get ...
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positions are filled at random form the 11 finalists, what is the probability of selecting: A: 3 females and 2 males? B: 4 females and 1... male? C: 5 females? D: At least 4 females? Problem 2 By examining the past driving records of drivers in a certain city, an insurance company has determined the following (empirical) probabilities: [pic] If a driver in this city is selected at random, what is the probability that: A: He or she drives less than 10,000 miles per year or has...
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cutting a deck of cards for $1,000. What is the probability that the card for the gambler will be the following? a. A face card – there are... 12 face cards in a deck of 52 cards. The probability would be 12/52 b. A queen – there are 4 queens in a deck, so the probability would be 4/52 c. A Spade - There are 13 cards of each suit so the probability is 13/52 or ¼. d. A jack of spades - There is only 1 jack of spades in a deck, so the probability would be 1/52 2. The employees in the textile...
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Mathematical Studies Project Probability of Blackjack Content Page... Page Statement of task 2 Introduction 3 - 4 Data collection 5 - 6 The four Blackjack strategies 7 - 15 Conclusion 16 Bibliography...
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Introduction The word Probability derives from probity, a measure of the authority of a witness in a legal case in Europe, and often... correlated with the witness's nobility. In a sense, this differs much from the modern meaning of probability, which, in contrast, is used as a measure of the weight of empirical evidence, and is arrived at from inductive reasoning and statistical inference. A short history of Probability Theory............ The branch of mathematics known as probability theory was inspired...
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advantages there would be way more trees therefor more and cleaner oxygen and disadvantages paper and all products made from... trees would not be the same if they wernt made out of trees Advantages: 1. Gives us shelter from the hot and humid sun 2. Holds the sand firm to the ground so that it will not be blown by the wind everywhere and the world will not become deserts. 3. Help stop global warming by reducing carbon dioxide by breathing it in and gives out oxygen. 4. Being a food producer which...
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Probability And Non Probability Sampling Cultural Studies Essay A probability sampling method is any method of... sampling that utilizes some form of random selection. In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen. Humans have long practiced various forms of random selection, such as picking a name out of a hat, or choosing the short straw. These days, we tend to...
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aware of the fact that basic math skills can be used anytime and anywhere. For instance, the mathematical usage of probability... can aid people in smart decision making, and can help people understand their odds. Statistically, probability refers to the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences (SOURCE). A rather obvious activity where probability applies is to is gambling. Casino games, such...
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Chapter 1 The Probability in Everyday Life In This Chapter Recognizing the prevalence and impact of probability in your... everyday life Taking different approaches to finding probabilities Steering clear of common probability misconceptions You’ve heard it, thought it, and said it before: “What are the odds of that happening?” Someone wins the lottery not once, but twice. You accidentally run into a friend you haven’t seen since high school during a vacation in Florida. A cop pulls you...
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classical and empirical probabilities. a. Classical probabilities are based on assumptions; Empirical... probabilities are based on observations. b. Classical probabilities do not require an action to take place; Empirical probabilities have to have been “performed”. 2) Gather 16 to 30 coins. Shake and empty bag of coins 10 times and tally up how many head and tails are showing. Number of coins: 20 * Consider the first toss, what is the observed probability of tossing a head? Of...
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Theoretical vs. Empirical Probability Probability- describes the chance that an uncertain event will occur. Empirical... Probability - estimate that the event will happen based on how often the event occurs after collecting the data or running an experiment. It is based specifically on direct observation or experiences. Empirical Probability Formula P(E) = probability that an event, E, will occur. Top = number of ways the specific event occurs. Bottom = number of ways the experiment...
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Subject : Probability and Statistics = PS Strand 1: Introduction to Statistics. Strand 2: Organizing Data. Strand 3 : Averages and Variation... Strand 4: Elementary Probability Theory. Strand 5: The Binomial Probability Distribution and Related Topics. Strand 6: Normal Distributions. Strand 7: Introduction to Sample Distributions. Benchmark Code Subject (M, S, SS, LA).Grade#.Strand#.Standard#. Benchmark# Example: PS.1.4.3 – Probability and Statistics, Strand 1, Standard 4, Benchmark 3 Strand: 1 INTRODUCTION...
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biggest baobab in South Africa is only 22 metres in height, but has a trunk that is 10.47 metres in diameter. It has a crown that is 38.2... metres in width. It is therefore almost twice as broad as it is tall! There is another baobab that is shorter, being only 17 metres in height, but having a trunk an incredible 15.9 metres thick! Its crown spreads to 37 metres in width. There are many other individual baobabs that approach or exceed 10 metres in trunk thickness. These trees have the greatest potential...
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MATH PORTFOLIO Modelling Probabilities on games of tennis Introduction: In this portfolio I shall investigate the different models... and probabilities based on the probabilities in the game of tennis. First I will start with the Part 1 of the portfolio where I will be concluding with the expected value and the standard distribution from my results. I will then take a look at the Non Extended play games where the highest of 7 points can be played. This is will be done with the use of...
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Essay On Trees Our Best Friends essay on trees our best friendsYou will have national immortality with the country through our... essay on trees our best friends dialogue. In social, older programs appear to have increased way in carrying particular, eternal markets to online constellation. Visible cloning is even high therapeutic cloning is only an profound essay on trees our best friends as it is held by a extraordinary man of parties; indeed, its term can be not justified. But for government...
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Probable Probability; Rolling Dice Statistics is based upon based upon common sense and logic, in a complex data.... Probability is just one of the many topics in statistical mathematics. It is used in our daily life, all over the world. Even games, require taking a chance and using probability to determine the predicted outcomes. Probability is the measure of how often a particular event will happen if something is done repeatedly, (596 Webster’s Dictionary). You cannot determine...
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accessing it in the next minute, what is the probability that a) Exactly 2 individuals will purchase an item? b) At least 2 individuals... will purchase an item? c) At most 2 individuals will purchase an item? 2. The quality Control Manager of ATV Cookies is inspecting a batch of chocolate-chip cookies that has been baked. If the production process is in control, the average number of chip parts per cookie is 6. What is the probability that in any particular cookie being inspected ...
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Chapter 2—Introduction to Probability PROBLEM 1. A market study taken at a local sporting goods store showed that of 20 people... questioned, 6 owned tents, 10 owned sleeping bags, 8 owned camping stoves, 4 owned both tents and camping stoves, and 4 owned both sleeping bags and camping stoves. Let: Event A = owns a tent Event B = owns a sleeping bag Event C = owns a camping stove and let the sample space be the 20 people questioned. a. Find P(A), P(B), P(C), P(A C), P(B C). ...
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These are used to make guesses or logical deductions about people or things. These deductions can be made according to the present, future... orpast. A) WILL and WON’T are used to express what we believe or guess to be true about the present. They indicate an assumption based on our knowledge of people and things, their routines, character, and qualities. Example: “I wonder what my husband is doing”. “Well, it’s Saturday night, so I guess that right now he’ll be dancing with a blonde woman at...
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and fetch the students and teachers to school especially when classes are abruptly suspended or cancelled because of the rains and floods that threaten the... safety of the individuals. It also stated in the bill that the Philippines and Brunei are the only countries in the Asia-Pacific region that open regular classes in June. Malaysia and Singapore open their classes in January, China in February, South Korea in March, Japan and India in April, Thailand in May, Indonesia in July and Hong Kong in September...
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[pic] TITILE : THEORY OF PROBABILITY NAME : KYRIOS JOYCE ERDAYA RAJOO IC NO : 930603-10-5700 CLASS : 5 MULIA TEACHER :... MRS.MALLIKA a) History of Probability The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical...
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to the market? 2) Developing a Model: MAI’s proposal directly gives Steve the conditional probabilities he needs -... probability of a successful venture given a favorable survey. Although the information from I&K is different, we can easily use Bayes’ theorem to on I&K information to compute the revised probabilities. As such, does not need any additional information from I&K. 3) Acquiring Input Data: Probabilities: Cost of introducing the products: $500,000 If successful the product line, increased...
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Teaching ideas for first conditional Maja Hadzic, Belgrade, Serbia 1. I usually give some examples of superstitions, e.g. If you break a... mirror, you will... (they give the answer, since they already know Future Simple Tense). 2. Then I give some more oral examples for them to finish. 3. After that they make their own examples. 4. Now they write down an example or two. 5. In groups they try to figure out what goes with the IF clause, what with the main clause. They report back to the class...
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4: Probability and Probability Distributions 4.1 a This experiment involves tossing a single die and observing the outcome.... The sample space for this experiment consists of the following simple events: E1: Observe a 1 E4: Observe a 4 E2: Observe a 2 E5: Observe a 5 E3: Observe a 3 E6: Observe a 6 b Events A through F are compound events and are composed in the following manner: A: (E2) D: (E 2) B: (E 2, E 4, E 6) E: (E...
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True/False Questions 1. The standard deviation of any normal random variable is always equal to one. Answer: False Type: Concept Difficulty: Easy... 2. For any normal random variable, the probability that the random variable will equal one is always zero. Answer: True Type: Concept Difficulty: Medium 3. The graph of a standard normal random variable is always symmetric. Answer: True Type: Concept Difficulty: Easy 4. The formula will convert any normal...
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1 PROBABILISTIC APPROACHES: SCENARIO ANALYSIS, DECISION TREES AND SIMULATIONS In the last chapter, we examined ways in which we can adjust... the value of a risky asset for its risk. Notwithstanding their popularity, all of the approaches share a common theme. The riskiness of an asset is encapsulated in one number – a higher discount rate, lower cash flows or a discount to the value – and the computation almost always requires us to make assumptions (often unrealistic) about the nature of risk...
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touching lives, making a difference Save Save Trees Save Environment Save Save Save Earth A TIL -CSR Initiative CSR touching... lives, making a difference Celebrating World Environment Day (WED) is about channeling individual actions that collectively become an exponential force for positive change. It’s all about being the change and take action for our generation and the next. WED is celebrated around the world in many ways that include street rallies, bicycle parades, green concerts...
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“The Trees” by Philip Larkin The trees are coming into leaf Like something almost being said; The recent buds relax and spread,... Their greenness is a kind of grief. Is it that they are born again And we grow old? No, they die too, Their yearly trick of looking of looking new. Is it written down in rings of grain. Yet still the unresting castles thresh In full grown thickness every May. Last year is dead, they seem to say, Begin afresh, afresh, afresh. Imagery to Larkin’s “The Trees” Voice...
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decision-maker to make decisions under risk or uncertainty. The concept of probability is fundamental to the use of the risk analysis... techniques. Hoe is probability defined? How are probabilities estimated? How are they used in the risk analysis techniques? How do statistical techniques help in resolving the complex problem of analyzing risk in capital budgeting? We attempt to answer these questions in our posts. Probability defined The most crucial information for the capital budgeting decision...
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Chapter 3 Probability True/False 1. A contingency table is a tabular summary of probabilities concerning two sets of... complementary events. Answer: True Difficulty: Medium 2. An event is a collection of sample space outcomes. Answer: True Difficulty: Easy 3. Two events are independent if the probability of one event is influenced by whether or not the other event occurs. Answer: False Difficulty: Medium 4. Mutually exclusive events have a nonempty...
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The Collier Encyclopedia’s definition for probability is the concern for events that are not certain and the reasonableness of one... expectation over another. These expectations are usually based on some facts about past events or what is known as statistics. Collier describes statistics to be the science of the classification and manipulation of data in order to draw inferences. Inferences here can be read to mean expectations, leading to the conclusion that the two go hand in hand in accomplishing...
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1. Use the sales forecaster’s predication to describe a normal probability distribution that can be used to approximate the... demand distribution. Sketch the distribution and show its mean and standard deviation. Let's assume that the expected sales distribution is normally distributed, with a mean of 20,000, and 95% falling within 10,000 and 20,000. We know that +/- 1.96 standard deviations from the mean will contain 95% of the values. So, we can get the standard deviation by: z = (x -...
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Probability and Statistics Research Project Name: Lakeisha M. Henderson ID: @02181956 Spring 2007 Abstract Table of Contents... Principle Component Analysis (PCA) Definition .4 Uses of PCA 5 Illustrative Example of PCA 5 Method to Determine PCA ..6 Basic Analysis of Variance (ANOVA) Purpose and Definition of ANOVA 12 Illustrative Example of ANOVA ...
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5.1 #12 , #34a. and b, #40, 48 #12. Which of the following numbers could be the probability of an event? 1.5, 0, = ,0 #34 More Genetics... In Problem 33, we learned that for some diseases, such as sickle-cell anemia, an individual will get the disease only if he or she receives both recessive alleles. This is not always the case. For example, Huntington’s disease only requires one dominant gene for an individual to contract the disease. Suppose that a husband and wife, who both have a dominant...
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resulting payoff in terms. Definition of 'Decision Tree' A schematic tree-shaped diagram used to determine a course of action or show a... statistical probability. Each branch of the decision tree represents a possible decision or occurrence. The tree structure shows how one choice leads to the next, and the use of branches indicates that each option is mutually exclusive. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining,...
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Available online at www.sciencedirect.com Procedia - Social and Behavioral Sciences 53 (2012) 106 – 114 SIIV - 5th International Congress - Sustainability... of Road Infrastructures Using Decision Trees to extract Decision Rules from Police Reports on Road Accidents López Griseldaa*, de Oña Juanb and Abellán Joaquínc a Ph. D. Student. TRYSE Research Group. Department of Civil Engineering, University of Granada, ETSI Caminos, Canales y Puertos, c/Severo Ochoa s/n, 18071, Granada, Spain a Ph. D....
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BY: Lillian Richard Hemp to Save Our Trees Worldwide we are seeing a devastation of our forests due to paper production. Consumption of... wood products has risen 64% since 1961. Globally, pulp for paper, has risen from 40% in 1998, to an expected 60% over the next 50 years. The industry expects that demand to double by 2050. The U.S. consumes 200,000,000 tons of wood products annually, increasing by 4% every year. U.S. paper producers consume 1 billion trees each year (735 pounds of paper for every...
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Summary Analysis of the poem, “Trees” by Alfred Joyce Kilmer LIFE of Alfred Joyce Kilmer American poet (1886-1918) Born: New Brunswick,... New Jersey Educated at: Rutgers College and Columbia University Milestones: From 1909 to 1917 he was on the staff of the New Standard Dictionary, as well as various periodicals. He was killed in France during World War I His lyric poem “Trees,” in the collection Trees and Other Poems (1914), won him popular recognition. His other works are Summer...
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Important Forest Trees And Their Uses ( Originally Published 1922 ) Of our native trees, the white pine is one of the best and... most valuable. It is a tall straight tree that grows to a height of 100 to 150 feet. It produces wood that is light in weight and easy to work because it is so soft. At ,one time there were extensive pine forests in the northeastern states. Many of the trees were very large, and occasionally one may still see pine stumps that are 5 to 6 feet in diameter. White pine made...
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A: True An inspector correctly identifies 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect... inspections is .736. A: Use Binomial table to discover , add 3 probabilities for 0,1,2 A continuous random variable may assume only integer values within a given interval. A: False A decision tree is a diagram consisting of circles decision nodes, square probability nodes and branches. A: False A table of random numbers must be normally distributed and...
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Assignment 3: PROBABILITY PROJECT Probability Project Strayer University Math 104 Professor Stephen Vest December... 16, 2012 In this writing assignment I will explain how I determined the odds of winning a Texas Hold’em game or not, where I have a six and seven of diamonds. My opponent has a ten of clubs and a ten of spades. At the turn or fourth street, the cards on the table are a three of diamonds, four of clubs, nine of spades, and a ten of diamonds. These cards show...
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Cynthia Johnson Period 3 Experiment 11: Electron Probability I. Statement of Purpose: We determined the hit... probability of a dart by throwing it onto a fixed target one hundred times. IV. Data* *Attached V. Results and Questions 1. (a) *Graph (b) The probability that the dart will hit in ring four is 16 out of 100. A dart will be most likely to hit the bulls-eye about 5 cm from it. (c) Our graph has a spike in hits on the ring...
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and larger as gains. In the following evaluation phase, people behave as if they would compute a value (utility), based on the potential... outcomes and their respective probabilities, and then choose the alternative having a higher utility. The formula that Kahneman and Tversky assume for the evaluation phase is (in its simplest form) given by where are the potential outcomes and their respective probabilities. v is a so-called value function that assigns a value to an outcome. The value function...
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3. Analyse the advantages and disadvantages of conditional fee arrangements for legal aid. A conditional fee arrangement is... basically a form of risk sharing whereby if the lawyer loses the case, the client does not have to pay. However, if the case is won, the lawyer can be recompensed through a success fee, which is worked out as a percentage of his cost. In the US, many cases have been funded this way but in English legal system conditional fee arrangement had been banned until the enactment...
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collection is being used here? a. An experiment. b. Direct observation. c. A survey. d. A census. 4. When the population is divided into... mutually exclusive sets, and then a simple random sample is drawn from each set, this is called: a. simple random sampling. b. stratified random sampling. c. cluster sampling. d. selection bias. 5. To give away a door prize, the host of a dinner party put each person's name into a hat, mixed them up, and selected one name. What sampling method was used? a. Simple random...
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Probability Distribution Memo To: Howard Gray, CEO; Jean Dubois, VP Mechanical Watch Division; Uma Gardner, VP Production; Amanda... Hamilton, VP Marketing After identifying the business problem of falling sales and an increase in rejections by the Swiss Official Chronometer Control, conducting a study for research will prove to identify a solution. Researchers performed a study of a sample population of 500 people. The study reveals 60% of the watches purchased are certified and the average...
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