Basic Probability Notes Probability— the relative frequency or likelihood that a specific event will occur. If the event is A, then the probability that A will occur is denoted P(A). Example: Flip a coin. What is the probability of heads? This is denoted P(heads). Properties of Probability 1. The probability of an event E always lies in the range of 0 to 1; i.e., 0 ≤ P( E ) ≤ 1. Impossible event—an event that absolutely cannot occur; probability is zero. Example: Suppose you roll a normal die...
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Conditional Probability How to handle Dependent Events Life is full of random events! You need to get a "feel" for them to be a smart and successful person. Independent Events Events can be "Independent", meaning each event is not affected by any other events. Example: Tossing a coin. Each toss of a coin is a perfect isolated thing. What it did in the past will not affect the current toss. The chance is simply 1-in-2, or 50%, just like ANY toss of the coin. So each toss is an Independent...
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PROBABILITY DISTRIBUTION In the world of statistics, we are introduced to the concept of probability. On page 146 of our text, it defines probability as "a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur" (Lind, 2012). When we think about how much this concept pops up within our daily lives, we might be shocked to find the results. Oftentimes, we do not think in these terms, but imagine what the probability of us getting behind...
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be able to ONEDefine probability. TWO Describe the classical, empirical, and subjective approaches to probability. THREEUnderstand the terms experiment, event, outcome, permutation, and combination. FOURDefine the terms conditional probability and joint probability. FIVE Calculate probabilities applying the rules of addition and multiplication. SIXUse a tree diagram to organize and compute probabilities. SEVEN Calculate a probability using Bayes theorem. What is probability There is really no answer...
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QMT200 CHAPTER 3: PROBABILITY DISTRIBUTION 3.1 RANDOM VARIABLES AND PROBABILITY DISTRIBUTION Random variables is a quantity resulting from an experiment that, by chance, can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous random variable. 3.2 DISCRETE RANDOM VARIABLE A random variable is called...
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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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Probability Paper David E. Nelson QNT/561 February 14, 2013 Professor Minh Bui Probability Paper My friends suggested that we take a hiking trip through South America this year. The reason for such a trip was to celebrate 16 years of close friendship. The four of us had known each other since we were in middle school and have since become inseparable. Even though we all lead very different lives and have even started our own families, we always manage to find time to spend with each other...
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Pilani Work-Integrated Learning Programmes Division Second Semester 2010-2011 Course Handout Course Number Course Title : AAOC ZC111 : Probability and Statistics Course E-mail address : aaoczc111@dlpd.bits-pilani.ac.in Course Description Probability spaces; conditional probability and independence; random variables and probability distributions; marginal and conditional distributions; independent random variables, mathematical exceptions, mean and variance, Binomial Poisson and normal distribution;...
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guys, this is the probability Assignment. Last date for submission is 10 aug... Q1. What is the probability of picking a card that was either red or black? Q2. A problem in statistics is given to 5 students A, B, C, D, E. Their chances of solving it are ½,1/3,1/4,1/5,1/6. What is the probability that the problem will be solved? Q3. A person is known to hit the target in 3 out of 4 shots whereas another person is known to hit the target in 2 out of 3 shots. Find the probability that the target...
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I. Probability Theory * A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance. * The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical theory of probability. One is the interpretation...
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P(S) The symbol for the probability of success P(F) The symbol for the probability of failure p The numerical probability of a success q The numerical probability of a failure P(S) = p and P(F) = 1 - p = q n The number of trials X The number of successes The probability of a success in a binomial experiment can be computed with the following formula. Binomial Probability Formula In a binomial experiment...
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variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi. The mean also of a random variable provides the long-run average of the variable, or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is , formally defined by Variance...
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random. What is the probability that at least one pair of shoes is obtained? 2. At a camera factory, an inspector checks 20 cameras and ﬁnds that three of them need adjustment before they can be shipped. Another employee carelessly mixes the cameras up so that no one knows which is which. Thus, the inspector must recheck the cameras one at a time until he locates all the bad ones. (a) What is the probability that no more than 17 cameras need to be rechecked? (b) What is the probability that exactly 17...
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EPGDIB 2014-16 Business statistics class exercise 1 Business application problems of probability Q1)Arthur Anderson enterprise group /National small business united ,Washington conducted a national survey of small business owners to determine the challenges for growth for their businesses. The top challenge selected by 46% of the small business owners was the economy. A close second was finding qualified workers (37%) .Suppose 15% of the small...
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The North Star Concert North Star.xls Best Guess, Worst Case, Best Case; and Continuous Uncertainties 3 Engine Services, Inc. Quick Start Guide to Crystal Ball Analyzing Uncertainty, Probability Distributions, and Simulation Learning Module: Crystal Ball Litigate Demo Engine Services.xls Language of Probability Distributions and Monte Carlo Simulation 4 Taurus Telecommunications Corporation: A New Prepaid Phone Card Learning Module: Tornado Sensitivity Taurus Telecommunications.xls Sensitivity...
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Probability 1.) AE-2 List the enduring understandings for a content-area unit to be implemented over a three- to five- week time period. Explain how the enduring understandings serve to contextualize (add context or way of thinking to) the content-area standards. Unit: Data and Probability Time: 3 weeks max Enduring Understanding: “Student Will Be Able To: - Know what probability is (chance, fairness, a way to observe our random world, the different representations) - Know what the...
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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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A Short History of Probability Dr. Alan M. Polansky Division of Statistics Northern Illinois UniversityHistory of Probability 2 French Society in the 1650’s ! Gambling was popular and fashionable ! Not restricted by law ! As the games became more complicated and the stakes became larger there was a need for mathematical methods for computing chances.History of Probability 3 Enter the Mathematicians ! A well-known gambler, the chevalier De Mere consulted Blaise Pascal ...
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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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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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regular soda, and two types of bottles of water. a. Suppose Evan chose a bottle from the refrigerator at random. Could we realistically say that the probability of choosing a diet soda is 7/3? Why or why not? b. If there are 16 total bottles of diet soda, 8 total bottles of regular soda, and 4 total bottles of water, what is the probability of each of the following: (i) Choosing a bottle of diet soda when a bottle is chosen at random (ii) Choosing a bottle of regular soda when a bottle is...
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PROBABILITY and MENDELIAN GENETICS LAB Hypothesis: If we toss the coin(s) for many times, then we will have more chances to reach the prediction that we expect based on the principle of probability. Results: As for part 1: probability of the occurrence of a single event, the deviation of heads and tails of 20 tosses is zero, which means that the possibility of heads and tails is ten to ten, which means equally chances. The deviation of heads and tails of 30 tosses is 4, which means that the...
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solved. C) a numerical measure of a probability experiment.. Ans = C D) a qualitative attribute of a population. 4) Given the table of probabilities for the random variable x, does this form a probability distribution? Answer yes or no. x 5 10 15 25 P(x) 0.1 –0.1 0.3 0.8 Ans = No 5) True or False: The expected value of a discrete random variable may be negative Ans = True 6) The table of probabilities of the random variable x is given...
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1/08/13 Probability Primer Principles of Econometrics, 4th Edition Probability Primer Page 1 ! Announcement: ! Please make sure you know who your tutor is and remember their names. This will save confusion and embarrassment later. ! Kai Du (David) ! Ngoc Thien Anh Pham (Anh) ! Zara Bomi Shroff Principles of Econometrics, 4th Edition Probability Primer Page 2 Chapter Contents ¡ P.1 Random Variables ¡ P.2 Probability Distributions ¡ P.3 Joint...
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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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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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respondent is selected at random, what is the probability that he or she a. prefers to order at the drive-through? b. is a male and prefers to order at the drive-through? c. is a male or prefers to order at the drive-through? d. Explain the difference in the results in (b) and (c). e. Given that a respondent is a male, what is the probability that he prefers to order at the drive-through? f. Given that a respondent is a female, what is the probability that she prefers to order at the drive-through...
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Probability Theory and Game of Chance Jingjing Xu April 24, 2012 I. INTRODUCTION Probability theory is the mathematical foundation of statistics, and it can be applied to many areas requiring large data analysis. Curiously, that the study on probability theory has its root in parlor games and gambling. In 17th century, dice gambling was a very common entertainment among the upper class. An...
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Tutorial on Discrete Probability Distributions Tutorial on discrete probability distributions with examples and detailed solutions. ------------------------------------------------- Top of Form | Web | www.analyzemath.com | | Bottom of Form | | Let X be a random variable that takes the numerical values X1, X2, ..., Xn with probablities p(X1), p(X2), ..., p(Xn) respectively. A discrete probability distribution consists of the values of the random variable X and their corresponding...
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infected. What is the probability that 3 randomly chosen client computers serviced by different servers (one per server) will all be infected? The probability that Alice’s RSA signature on a document is forged is () What is the probability that out of 4 messages sent by Alice to Bob at least one is not forged? Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible with Event A. What is the probability of getting 6 tails in...
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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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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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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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| | | |Review of Probability Concepts | | | |Fundamental Concepts | | | |Bayes’s Theorem | | | |Random Variables & Probability Distribution |...
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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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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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M227 Chapter 1 Nature of Probability and Statistics OBJECTIVES Demonstrate knowledge of statistical terms. Differentiate between the two branches of statistics. Identify types of data. Identify the measurement level for each variable. Identify the four basic sampling techniques. Explain the difference between an observational and an experimental study. Explain how statistics can be used and misused. Explain the importance of computers and calculators in statistics. Statistics is the science...
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it is in his or her best interest to do so. ABNORMAL RETURNS: A term used to describe the returns generated by a given security or portfolio over a period of time that is different from the expected rate of return. The expected rate of return is the estimated return based on an asset pricing model, using a long run historical average or multiple valuations. FACTOR ANALYSIS: Factor analysis is a statistical procedure used to uncover relationships among many variables. This allows numerous intercorrelated...
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Profit Rate[7][8] :::OR ::: Operating margin, Operating Income Margin, Operating profit margin or Return on sales (ROS)[8][9] Note: Operating income is the difference between operating revenues and operating expenses, but it is also sometimes used as a synonym for EBIT and operating profit.[10] This is true if the firm has no non-operating income. (Earnings before interest and taxes / Sales[11][12]) Profit margin, net margin or net profit margin[13] Return on equity (ROE)[13] Return...
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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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Chapter 6 Continuous Probability Distributions Case Problem: Specialty Toys 1. Information provided by the forecaster At x = 30,000, [pic] [pic] Normal distribution [pic] [pic] 2. @ 15,000 [pic] P(stockout) = 1 - .1635 = .8365 @ 18,000 [pic] P(stockout) = 1 - .3483 = .6517 @ 24,000 [pic] P(stockout) = 1 - .7823 = .2177 @ 28,000 [pic] ...
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A Course In Business Statistics 4th Edition Chapter 4 Using Probability and Probability Distributions A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. Chap 4-1 Important Terms Probability – the chance that an uncertain event will occur (always between 0 and 1) Experiment – a process of obtaining outcomes for uncertain events Elementary Event – the most basic outcome possible from a simple experiment Sample Space – the collection of all possible ...
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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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Temperature is an example of a variable that uses a. the ratio scale b. the interval scale c. the ordinal scale d. either the ratio or the ordinal scale 2. The nominal scale of measurement has the properties of the a. ordinal scale b. only interval scale c. ratio scale d. None of these alternatives is correct. 3. Statistical studies in which researchers control variables of interest are a. experimental studies b. control observational studies c. non-experimental studies ...
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Worksheet 5 (Chapter 3): Probability II Name: ______________________________________________ Section: _________________________ For any of the following questions be sure to show appropriate work and give appropriate probability statements. 1. Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. Intended Enrollment Status ...
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------------------------------------------------- ------------------------------------------------- Research Paper ------------------------------------------------- THE PROBABILITY OF FINANCIAL CRISIS IN THE USA IN 2012-2013 ------------------------------------------------- Ilias Habbasov ------------------------------------------------- ------------------------------------------------- BBA course submitted to Elżbieta Jendrych, PhD on 3 December 2012 Winter Semester 2012/2013 ...
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BBA (Fall - 2014) Business Statistics Theory of Probability Ahmad Jalil Ansari Business Head Enterprise Solution Division Random Process In a random process we know that what outcomes or events could happen; but we do not know which particular outcome or event will happen. For example tossing of coin, rolling of dice, roulette wheel, changes in valuation in shares, demand of particular product etc. Probability It is the numeric value representing the chance, likelihood, or possibility...
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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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results from 100 strands are as follows: High conductivity Low conductivity Strength High Low 74 8 15 3 (a) If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high? P (High conductivity and high strength)= 74/100 =0.74 (b) If a strand is randomly selected, what is the probability that its conductivity is low or its strength is low? P (Low strength or low conductivity) = P(Low conductivity) + P(Low strength) – P(Low conductivity and low...
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You have only two qualitatively different outcomes possible. Count the number of ways to get each of the two. FORMULA: nCr = n! / r!(n-r)! SOLUTION: There are just two possible outcomes here: the two missing socks make a pair (the best case) and the two missing stocks do not make a pair (the worst case). The total number of deferent outcomes (the ways to choose the missing socks) is 10c2= 45. The number of best-case ones is 5; hence its probability is 5/45 =...
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Week Four Discussion 2 1. In your own words, describe two main differences between classical and empirical probabilities. The differences between classical and empirical probabilities are that classical assumes that all outcomes are likely to occur, while empirical involves actually physically observing and collecting the information. 2. Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between 16 and 30. You do not...
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Probability Concepts 1. Fundamental Concepts of Probability 2. Mutually Exclusive and Collectively Exhaustive 3. Statistically Independent and Dependent Events 4. Bayes’Theorem Learning Objectives • Understand the basic foundations of probability analysis • Learn the probability rules for conditional probability and joint probability • Use Bayes’ theorem to establish posterior probabilities Reference: Text Chapter 2 Introduction • Life is uncertain; we are note sure what the ...
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Descriptive Statistics and Probability Distribution Problem Sets Emily Noah QNT561 Anthony Matias December 24, 2012 Descriptive Statistics and Probability Distribution Problems Sets Descriptive statistics and probability distribution is two ways to find information with certain data giving. In Descriptive statistics the data can give a mode, mean, median, and range by the numerical information, which is giving to find the information. In probability distribution the data is collected and...
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campaign . From this model it should be possible to predict the profitability of a prospective donor , hence allowing a more targeted campaign at lower cost . The difficulty is due to extremely imbalanced data and the inverse correlation between the probability of response and the dollar amount generated from it . The available data set and problem is of the KDD-CUP-98 challenge . The solution would be applicable to any direct marketing campaign which has historical data available . Table of Contents ...
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Conditional Sentences / If-Clauses Type I, II und III Conditional Sentences are also known as Conditional Clauses or If Clauses. They are used to express that the action in the main clause (without if) can only take place if a certain condition (in the clause with if) is fulfilled. There are three types of Conditional Sentences. Conditional Sentence Type 1 → It is possible and also very likely that the condition will be fulfilled. Form: if + Simple Present, will-Future Example: If I find her...
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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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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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University of Perpetual Help System Dalta Molino Campus Molino III, Bacoor City Probability and Statistics LAGERA, Einar John A. Table of Contents Simple Correlation Analysis ................................................................................................. 1 Introduction .................................................................................................................................................................. 1 What is Correlation? ..............
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This Lesson Problem 1 Four friends take an IQ test. Their scores are 96, 100, 106, 114. Which of the following statements is true? I. The mean is 103. II. The mean is 104. III. The median is 100. IV. The median is 106. (A) I only (B) II only (C) III only (D) IV only (E) None is true Solution The correct answer is (B). The mean score is computed from the equation: Mean score = Σx / n = (96 + 100 + 106 + 114) / 4 = 104 Since there are an even number of scores (4 scores), the median is the average...
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