5—DISCRETE PROBABILITY DISTRIBUTIONS MULTIPLE CHOICE 1. A numerical description of the outcome of an experiment is called a a. descriptive statistic b. probability function c. variance d. random variable ANS: D PTS: 1 TOP: Discrete Probability Distributions 2. A random variable that can assume only a finite number of values is referred to as a(n) a. infinite sequence b. finite sequence c. discrete random variable d. discrete probability function ANS: C PTS: 1 TOP: Discrete Probability Distributions
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Outline 4 Probability – the chance that an uncertain event will occur (always between 0 and 1) Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1) Assessing Probability probability of occurrence= probability of occurrence based on a combination of an individual’s past experience, personal opinion, and analysis of a particular situation Events Simple event
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5 Supply Chain Management Based on Modeling & Simulation: State of the Art and Application Examples in Inventory and Warehouse Management Francesco Longo Modeling & Simulation Center – Laboratory of Enterprise Solutions (MSC-LES) Mechanical Department, University of Calabria Via P. Bucci, Cubo 44C, third floor, 87036 Rende (CS) Italy 1. Introduction The business globalization has transformed the modern companies from independent entities to extended enterprises that strongly cooperate with all
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Probability review (week 2) 1 Bernoulli, Binomial, Poisson and normal distributions. In this excercise we deal with Bernoulli, binomial, Poisson and normal random variables (RVs). A Bernoulli RV X models experiments, such as a coin toss, where success happens with probability p and failure with probability 1 − p. Success is indicated by X = 1 and failure by X = 0. Therefore, the probability mass function (pmf) of X is P {X = 0} = 1 − p, P {X = 1} = p (1) A binomial random variable (RV)
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5 1. Let X be a random variable with probability density function c(1 − x2 ) −1 < x < 1 0 otherwise ∞ f (x) = (a) What is the value of c? We know that for f (x) to be a probability distribution −∞ f (x)dx = 1. We integrate f (x) with respect to x, set the result equal to 1 and solve for c. 1 1 = −1 c(1 − x2 )dx cx − c x3 3 1 −1 = = = = c = Thus, c = 3 4 c c − −c + c− 3 3 2c −2c − 3 3 4c 3 3 4 . (b) What is the cumulative distribution function of X? We want to ﬁnd F (x).
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introduce students to the principles, uses and interpretation of regression analysis most commonly employed in applied economics; to provide participants with sufficient knowledge of regression methods to critically evaluate and interpret empirical research. On completion of this module students should be able to: demonstrate understanding of the assumptions and properties underlying regression analysis and the principle of ‘least squares’; interpret and manipulate the coefficients of multiple regression
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for women. Distribution of Individuals by Gender Gender Percentage Females 48% Males 52% Tenure with Company Distribution by Gender Under 2 years 2-5 Years Over 5 years Male 11 5 7 Female 12 5 4 Percentage of the Survey Participants in Each Department Department Percentage Information Technology 34% Human Resources 25% Administration 41% Mean for Extrinsic Value by Gender Gender Mean Extrinsic Value Male 5.33 Female 5.41 The probabilities we looked at
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Probability & Statistics for Engineers & Scientists This page intentionally left blank Probability & Statistics for Engineers & Scientists NINTH EDITION Ronald E. Walpole Roanoke College Raymond H. Myers Virginia Tech Sharon L. Myers Radford University Keying Ye University of Texas at San Antonio Prentice Hall Editor in Chief: Deirdre Lynch Acquisitions Editor: Christopher Cummings Executive Content Editor: Christine O’Brien Associate Editor: Christina Lepre Senior
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retails channel, but sells its PCs directly to customers through its website, Dell.com, as Figure 4 shows. This way the intermediary steps that may add time and cost are eliminated, and Dell is directly linked to its customers. Figure 4: Distribution channel of Dell vs. a traditional company [31] In fact, Dell sells directly to all its customers, “from home-PC users to the world’s largest corporations” [54]. This way it creates a direct relationship with each individual customer, which
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Probability and Statistics for Finance The Frank J. Fabozzi Series Fixed Income Securities, Second Edition by Frank J. Fabozzi Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. Abate Handbook of Global Fixed Income Calculations by Dragomir Krgin Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi Real Options and Option-Embedded Securities by William T. Moore Capital Budgeting: Theory and Practice by Pamela P. Peterson
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What are the two basic laws of probability? What are the differences between a discrete probability distribution and a continuous probability distribution? Provide at least one example of each type of probability distribution. The two basic laws of probability are adding mutually exclusive events and addition for events that are not mutually exclusive (Render, Stair & Hanna, 2008). The probability must be between zero and one for any event just as the sum must equal one of all the events. Therefore
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Probability, Mean and Median In the last section, we considered (probability) density functions. We went on to discuss their relationship with cumulative distribution functions. The goal of this section is to take a closer look at densities, introduce some common distributions and discuss the mean and median. Recall, we define probabilities as follows: Proportion of population for Area under the graph of p ( x ) between a and b which x is between a and b p( x)dx a b The cumulative
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Simulation: Definition • Simulation is a mathematical model of a real system. • The system consists of inputs and outputs and a mathematical expression. • We obtain the outputs by manipulation of the inputs using the mathematical expression. Simulation Model Risk Analysis: Example • PortaCom manufactures printers. • These parameters apply: – Selling price = 249 per unit – Administrative Cost = 400,000 – Advertising cost = 600,000 • Cost of direct labor, cost of parts, and the 1st year
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use of Simulation by Managers of various organizations. Under discussion will be: Definition of simulation. Model construction. When and why it becomes handy to use simulation. Steps used in simulation technique. Random selection in simulation. Advantages / benefits derived from use of simulation technique. Disadvantages /Challenges associated with simulation technique. Role of computer in simulation. Conclusion / comments. Definition of simulation: Simulation can be
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The reflection of my experiences of The Everest group simulation z3238040 Seung Kon Back ● The Executive Summary The team 1 was organised to perform two Everest simulations and its members were Seungkon, Florence, Yajia, Michael, Manas and Rebecca. This report is a record of experiences during the simulations and also aims to describe the team’s experiences and critically analyse the results and communication structures. It was found that the main factor of the team’s failure is attributable
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4/27/2014 MA3110 Statistics Otis Jackson Unit 4 problem set 1: Normal Probability Distributions Page.285 Ex 6,8,10,12 6. x = 80, z=80-10015 = -1.33 z= 0.0918 1-0.0918 = 0.9082 8. x = 110, z=110-10015 = 0.67 z= 0.7486 z= 75-10015 = -1.67 z= 0.0475 0.7486-0.0475= 0.7011 (shaded area) 10. z= 0.84 (shaded) z= -0.84 x= 100+(-0.84∙15) = 87 (rounded) 12. . z= 2.33 x= 100+(2.33∙15) = 135 (rounded) Page 288 Ex 34 34.Appendix B Data Set: Duration of Shuttle Flights a
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covered market planning strategy, market segmentation, market research and pricing strategy, featuring a simulation of market segmentation, created by Forio in partnership with Harvard Business School Publishing. Forio is one of the leading companies in online simulations, boasting an impressive international clientele, including top universities and government agencies. The company’s offering includes Simulate™, a free tool to build simulations online with drag-and-drop interface and several import features
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Probability and Distributions Abstract This paper will discuss the trends and data values and how they relate to statistical terms. Also will describe the probability of different actions to the same group of data. The data will be broke down accordingly to qualitative and quantitative data, and will be grouped and manipulated to show how the data in each group can prove to be useful in the workplace. Memo To: Head of American Intellectual Union From: Abby Price Date: 3/05/2014
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Simulation Analysis Danielle B. Western Governors University Simulation Analysis Introduction In the following information below I will discuss many elements of decisions that were made while completing the Business Fundamentals Marketplace Simulation by Innovative Learning Solutions. These elements include, product design decisions, target markets, sales office locations, marketing research, international markets, and considerations for a heavy international commitment. Product Design
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looking for research data about Gender, Probability factors and several other data sets that they need to use for reporting purposes. This data will help the AIU make sound and responsible decisions in regards to the data that they are looking to collect. Memo To: Director, American Intellectual Union From: John C. Carter Date: 8/2/2014 Subject: Distribution and Probability of data collected Dear Sir: As we discussed in earlier meetings, the AIU is looking for research data to
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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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Assignment 2 Problem 1: Question 1. The probability of a case being appealed for each judge in Common Pleas Court. p(a) | 0.04511031 | 0.03529063 | 0.03497615 | 0.03070624 | 0.04047164 | 0.04019435 | 0.03990765 | 0.04427171 | 0.03883194 | 0.04085893 | 0.04033333 | 0.04344897 | 0.04524181 | 0.06282723 | 0.04043298 | 0.02848818 | Question 2. The probability of a case being reversed for each judge in Common Pleas Court. P® | 0.00395127 | 0.0029656 | 0.0063593
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PROBABILITY 1. ACCORDING TO STATISTICAL DEFINITION OF PROBABILITY P(A) = lim FA/n WHERE FA IS THE NUMBER OF TIMES EVENT A OCCUR AND n IS THE NUMBER OF TIMES THE EXPERIMANT IS REPEATED. 2. IF P(A) = 0, A IS KNOWN TO BE AN IMPOSSIBLE EVENT AND IS P(A) = 1, A IS KNOWN TO BE A SURE EVENT. 3. BINOMIAL DISTRIBUTIONS IS BIPARAMETRIC DISTRIBUTION, WHERE AS POISSION DISTRIBUTION IS UNIPARAMETRIC ONE. 4. THE CONDITIONS FOR THE POISSION MODEL ARE : • THE PROBABILIY
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The t-Distribution Characteristics of the t-distribution similar to the normal distribution 1. It is bell-shaped. 2. It is symmetric about the mean. 3. The mean, median, and mode are equal to 0 and are located at the centre of the distribution. 4. The curve never touches the x axis. Characteristics of the t-distribution that differ from the normal distribution 1. The variance is greater than 1. 2. The t-distribution is a family of curves based on the concept of degrees of freedom, which
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For Students Solutions to Odd-Numbered End-of-Chapter Exercises * Chapter 2 Review of Probability 2.1. (a) Probability distribution function for Y Outcome (number of heads) | Y 0 | Y 1 | Y 2 | Probability | 0.25 | 0.50 | 0.25 | (b) Cumulative probability distribution function for Y Outcome (number of heads) | Y 0 | 0 Y 1 | 1 Y 2 | Y 2 | Probability | 0 | 0.25 | 0.75 | 1.0 | (c) . Using Key Concept 2.3: and so that 2.3. For the two new random
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Brooklyn Warren Chapter 10 Simulation Modeling What is Simulation? * To try to duplicate the features, appearance, and characteristics of a real system. * Imitate a real-world situation mathematically. * Study its properties and operating characteristics. * Draw conclusions and make action decisions based on the results. Processes of Simulation: 1. Define Problem 2. Introduce Important Variables 3. Construct Simulation Model 4. Specify Values of Variables
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Probability Discrete Event Simulation: Tutorial on Probability and Random Variables 1. A card is drawn from an ordinary deck of 52 playing cards. Find the probability that it is (a) an Ace, (b) a jack of hearts, (c) a three of clubs or a six of diamonds, (d) a heart, (e) any suit except hearts, (f) a ten of spade, (g) neither a four nor a club (1/3, 1/52, 1/26, 1/4, 3/4, 4/13, 9/13) 2. A ball is drawn at random from a box containing six red balls, 4 white balls and 5 blue balls. Determine
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Barber’s Shop Simulation Report Description of the system and its operation: A barber shop opens from 9am to 5pm every day for six days a week. The shop has two barbers and one receptionist. Customers arrive randomly. When a customer arrives, he needs to first register with the receptionist and the receptionist helps him to put on a special gown to protect his own clothes from hair. The process for registration and putting on the gown together takes a short fixed time. There are totally 10
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PROBABILITY ASSIGNMENT 1. The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the US are using their seat belts. Sample data consistent with the NHTSA survey are as follows. (Data as on May, 2015) Driver using Seat Belt? | Region | Yes | No | Northeast | 148 | 52 | Midwest | 162 | 54 | South | 296 | 74 | West | 252 | 48 | Total | 858 | 228 | a. For the U.S., what is the probability that the driver is using
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Probability Distribution in Research Simulation Sheil Merrill RES/341 August 16, 2011 Richard Harrell Aquine is ready to take a greater share of the chronometer market. As you know the chronometer market is the highest priced watch market with chronometers being sold for more than five thousand dollars. It is Aquine’s goal to compete with the established chronometer manufacturers Zweiger, Scheobel, and Waechter. This was the primary reason why Chief Executive Officer Howard Gray hired
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2009 World Congress on Computer Science and Information Engineering Simulation and Research on Data Fusion Algorithm of the Wireless Sensor Network Based on NS2 Junguo Zhang, Wenbin Li, Xueliang Zhao, Xiaodong Bai, Chen Chen Beijing Forestry University, 35 Qinghua East Road, Haidian District,Beijing, 100083 P.R.China information which processed by the embedded system to the user terminals by means of random selforganization wireless communication network through multi-hop relay. Thus it
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SIMULATION DESCRIPTION: As the manager of TriState Dairies market research department, you need to determine what to do with the Dairies' surplus milk. You earned 69 percent. Background TriState Dairies is a food processor that packages and sells dairy products. At present their core business is selling 1) pasteurized, skimmed, and plain milk, and 2) yogurts and yogurt drinks. They want to expand their market, particularly for milk. They can easily convert surplus milk production to the
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discussing the laws of probability so, in the laws of the probability we have a random experiment, as a consequence of that we have a sample space, we consider a subset of the, we consider a class of subsets of the sample space which we call our event space or the events and then we define a probability function on that. Now, we consider various types of problems for example, calculating the probability of occurrence of a certain number in throwing of a die, probability of occurrence of certain
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Monte Carlo Simulation The Monte Carlo Simulation encompasses “any technique of statistical sampling employed to approximate solutions to quantitative problems” (Monte Carlo Method, 2005). The Monte Carlo method simulates the full system many times, each randomly choosing a value for each variable from its probability distribution. The outcome is a probability distribution of the overall value of the system calculated through the iterations of the model. A standard approach to risk management
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7.10.2015 г. 1 1. Experiment, Outcomes, and Sample space 2. Random Variables 3. Probability Distribution of a Discrete Random Variable 4. The Binomial Probability Distribution 5. The Hypergeometric Probability Distribution 6. The Poisson Probability Distribution 7. Continuous Random Variables 8. The Normal Distribution 9. The Normal Approximation to the Binomial Distribution 2 1 7.10.2015 г. An experiment is a process that, when performed, results in one and only one
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Thinking Critically Simulation Professor Douglas Reed University of Phoenix 07/31/11 The primary tools provided in the critical thinking and decision-making simulation included research analysis provided by the organization and a decision-making matrix. Although these tools provided the framework for applying critical thinking activities they did not provide the additional tools to support long-term goals. Starting with assessing the problem, the research provided several issues with varying
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In “Are you living in a computer simulation?”, Nick Bostrom presents a probabilistic analysis of the possibility that we might all be living in a computer simulation. He concludes that it is not only possible, but rather probable that we are living in a computer simulation. This argument, originally published in 2001, shook up the field of philosophical ontology, and forced the philosophical community to rethink the way it conceptualizes “natural” laws and our own intuitions regarding our existence
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Unit 2 – Probability and Distributions Kimberly Reed American InterContinental University Abstract This week’s paper focuses on an email that will be written to AUI the email will contain information from the data set key and explain why this information is important to the company. Memo To: HR Department From: Senior Manager Date: 20 Sept, 2011 Subject: Data Set Dear Department Heads: The following memo will contain information that contains vital and confidential information
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Title: The Probability that the Sum of two dice when thrown is equal to seven Purpose of Project * To carry out simple experiments to determine the probability that the sum of two dice when thrown is equal to seven. Variables * Independent- sum * Dependent- number of throws * Controlled- Cloth covered table top. Method of data collection 1. Two ordinary six-faced gaming dice was thrown 100 times using three different method which can be shown below. i. The dice was held in
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Probability for Engineers (IHE 6120) Report On Probabilistic Analysis on Revenue generation by Electronic Retailers for five consecutive years Submitted
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CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao,David Tse Note 11 Conditional Probability A pharmaceutical company is marketing a new test for a certain medical condition. According to clinical trials, the test has the following properties: 1. When applied to an affected person, the test comes up positive in 90% of cases, and negative in 10% (these are called “false negatives”). 2. When applied to a healthy person, the test comes up negative in 80% of cases
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Their statistics show that an accident prone person will have accident within a year with probability 0.4, whereas probability decreases to 0.2 for a non-accident prone person. If 30% of population is accident prone, what is the probability that a new policy holder will have an accident within one year of purchasing the policy? Suppose a new policy holder has an accident within one year, what is the probability that he or she is accident prone? Q2. Surveys by the Federal Deposit Insurance Corporation
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Probability Distributions Individual Project Tammy Lynn Ayers AIU Online American Inmates Union Data Collection Results Submitted by Tammy Lynn Ayers On November 27, 2011 Dear Mr. Smith, We administered a survey to our inmates in order to measure their satisfaction with their incarceration. From this survey, we collected nine different sections of data. They include: gender, age, types of offense, type of facility, length of sentence, satisfaction with criminal justice system
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Using Probability Distribution in Research Jorge Uria RES 341 November 28, 2011 Walter Deckert Background Aquine has been losing market share in the mechanical watch division for the past three years and now stands at five percent. There are different views as to what the reasons for the decline are with some members of management indicating that the quality of manufacture is the problem and others that the advertising strategy is to blame. Research and analysis was conducted on processes
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Introduction to Managerial Accounting AIU Online Abstract This paper is going to cut cost for an uptown clinic. It will tell where the cuts should take place in order not to hurt the day to day functioning of the clinic. It will describe how managerial accounting is different from cost accounting and describe the lean production philosophy. It will compare and contrast accounting principles in lean production to those of typical production. The paper will advise the Dr.on how to prepare for
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Proposing a Research Agenda for Swedish Sawmill Distribution Channel Challenges Åsa Gustafsson asa.gustafsson@lnu.se Lars-Olof Rask lars-olof.rask@lnu.se School of Engineering Linnaeus University, Växjö, Sweden Abstract Purpose; The purpose of this study is to identify distribution channel research needs given the variety of distribution channel challenges among Swedish sawmill companies. Design / methodology / approach; Explorative case study research Findings: The paper proposes a typology
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Probability XXXXXXXX MAT300 Professor XXXXXX Date Probability Probability is commonly applied to indicate an outlook of the mind with respect to some hypothesis whose facts are not yet sure. The scheme of concern is mainly of the frame “would a given incident happen?” the outlook of the mind is of the type “how sure is it that the incident would happen?” The surety we applied may be illustrated in form of numerical standards and this value ranges between 0 and 1; this is referred to
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PROBABILITY SEDA YILDIRIM 2009421051 DOKUZ EYLUL UNIVERSITY MARITIME BUSINESS ADMINISTRATION CONTENTS Rules of Probability 1 Rule of Multiplication 3 Rule of Addition 3 Classical theory of probability 5 Continuous Probability Distributions 9 Discrete vs. Continuous Variables 11 Binomial Distribution 11 Binomial Probability 12 Poisson Distribution 13 PROBABILITY Probability is the branch of mathematics that studies the possible outcomes of given events together
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Probability Question 1 The comparison between the bar chart and histogram are bar graphs are normally used to represent the frequency of discrete items. They can be things, like colours, or things with no particular order. But the main thing about it is the items are not grouped, and they are not continuous. Where else for the histogram is mainly used to represent the frequency of a continuous variable like height or weight and anything that has a decimal placing and would not be exact in other
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minutes Introduction to Probability 1 Probability Probability will be the topic for the rest of the term. Probability is one of the most important subjects in Mathematics and Computer Science. Most upper level Computer Science courses require probability in some form, especially in analysis of algorithms and data structures, but also in information theory, cryptography, control and systems theory, network design, artiﬁcial intelligence, and game theory. Probability also plays a key role in ﬁelds
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