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...CHAPTER 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 3. A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a a. uniform probability distribution b. binomial probability distribution c. hypergeometric probability distribution d. normal probability distribution ANS: B PTS: 1 TOP: Discrete Probability Distributions 4. Variance is a. a measure of the average, or central value of a random variable b. a measure of the dispersion of a random variable c. the square root of the standard deviation d. the sum of the squared deviation of data elements from the mean ANS: B PTS: 1 TOP: Discrete Probability Distributions 5. A continuous random variable may assume a. any value in an interval or collection of intervals b. only integer values in an interval or collection of intervals c. only fractional values in an interval or collection of intervals d. only the positive integer values in an interval ANS: A PTS: 1 TOP:......

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...Statistics 100A Homework 5 Solutions Ryan Rosario Chapter 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). To do that, integrate f (x) from the lower bound of the domain on which f (x) = 0 to x so we will get an expression in terms of x. x F (x) = −1 c(1 − x2 )dx cx − cx3 3 x −1 = But recall that c = 3 . 4 3 1 3 1 = x− x + 4 4 2 = 3 4 x− x3 3 + 2 3 −1 < x < 1 elsewhere 0 1 4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by, 10 x2 f (x) = (a) Find P (X > 20). 0 x > 10 x ≤ 10 There are two ways to solve this problem, and other problems like it. We note that the area we are interested in is bounded below by 20 and unbounded above. Thus, ∞ P (X > c) = c f (x)dx Unlike in the discrete case, there is not really an advantage to using the complement, but you can of course do so. We could consider P (X > c) = 1 − P (X < c), c P (X > c) = 1 − P (X < c) = 1 − −∞ f (x)dx P (X > 20) = 10 dx......

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...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. Find the mean and standard deviation, and verify that the data have a distribution that is roughly normal. Mean= 25317115 = 220.15 Standard Deviation=115253172-(25317)2115(115-1) = 86 (rounded) The normal distribution is 115 b. Treat the statistics from part (a) as if they are population parameters and assume a normal distribution to find the values of the quartiles 1,2 and 3. Mean= 220.15 Standard Deviation= 86 Q1 = 220.5 + (-0.67 ∙ 86)= 162.53 Q2= 220.5 + (0.00 ∙ 86) = 220.5 Q3=220.5 + (0.67 ∙ 86) = 277.77 Page.300 Ex 20 Quality Control: Sampling Distribution of Proportion after constructing a new manufacturing machine. 5 prototype integrated circuit chips are produced and it is found that 2 are defective (D) and 3 are acceptable (A). Assume that two if the chips are randomly selected with replacement from this population a. After identifying the 25 different possible samples, find the proportion of defects in each of them, then use a table to describe the sampling distribution of the proportions......

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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 Subject: Data analysis from within the union’s surveys Dear Dr. Common: I will be analyzing data given to me which was taken from a survey within the union from 186 employees. I will discuss probability and how its information is important in the workplace. Overview of the Data Set The data group I was given to analyze has 9 categories: gender, age, department, position, tenure, job satisfaction, intrinsic, extrinsic, and benefits. The employees were asked to rate on a scale of 1-7 on how satisfied they were with the company. Gender, age, department, position and tenure are all qualitative data. This data is acknowledged by a code on the given data but cannot measured unlike the quantitative data: job satisfaction, intrinsic, extrinsic, and benefits. Use of Statistics and Probability in the Real World Statistics are just about everywhere in the business world, from the upper management to the lower line of employees, statistics are very useful and are a huge part of......

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...of the American Intellectual Union (AIU) is 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 help provide clear and concise numbers that you will be able to use in your business. These numbers that will be included in this document will allow the AIU to make sound and responsible business decisions about the future of your company. Overview of the Data Set The data that was used in this report came from information collected by AIU. These data sets include: Gender, Age, Department, Position, Tenure, Job Satisfaction, Intrinsic, Extrinsic and Benefits. With this data we will be looking at job satisfaction and how it relates to the different data sets that are included. These data sets include some Quantitive data sets like; Gender, Age and Tenure and Intrinsic. They also include a set of Qualitative categories like Department, Position, Extrinsic and Benefits. Use of Statistics and Probability in the Real World Statistics and Probability are used in a wide variety of ways in the modern workplace. Being able to read......

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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 is related to sample size. 3. As the sample size increases, the t- distribution approaches the standard normal distribution. Characteristics of the Chi-Square Distribution 1. It is not symmetric. 2. The values of χ2 are non-negative (i.e. χ2 > 0). 3. The chi-square distribution is asymptotic to the horizontal axis on the right-hand-side. 4. The shape of the chi-square distribution depends upon the degrees of freedom. 5. As the number of degrees of freedom increases, the chi-square distribution becomes more symmetric (normal distribution). 6. Total area under the curve is equal to 1. 7. Degrees of freedom = (no. of rows – 1)*(no. of col. – 1). The F Distribution 1) The F distribution is an asymmetric distribution that has a minimum value of 0, but no maximum value. 2) The curve reaches a peak not far to the right of 0, and then gradually approaches the horizontal axis, but never quite touches the horizontal axis. 3) The F distribution has two degrees of......

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...RES 341 Week 5 Individual Assignment Using Probability Distribution in Research Simulation Get Tutorial by Clicking on the link below or Copy Paste Link in Your Browser http://hwguiders.com/downloads/res-341-week-5-individual-assignment-using-probability-distribution-research-simulation/ For More Courses and Exams use this form ( http://hwguiders.com/contact-us/ ) Feel Free to Search your Class through Our Product Categories or From Our Search Bar (http://hwguiders.com/ ) RES 341 Week 5 Individual Assignment Using Probability Distribution in Research Simulation Get Tutorial by Clicking on the link below or Copy Paste Link in Your Browser http://hwguiders.com/downloads/res-341-week-5-individual-assignment-using-probability-distribution-research-simulation/ For More Courses and Exams use this form ( http://hwguiders.com/contact-us/ ) Feel Free to Search your Class through Our Product Categories or From Our Search Bar (http://hwguiders.com/ ) RES 341 Week 5 Individual Assignment Using Probability Distribution in Research Simulation Get Tutorial by Clicking on the link below or Copy Paste Link in Your Browser http://hwguiders.com/downloads/res-341-week-5-individual-assignment-using-probability-distribution-research-simulation/ For More Courses and Exams use this form ( http://hwguiders.com/contact-us/ ) Feel Free to Search your Class through Our Product Categories or From Our Search Bar (http://hwguiders.com/ ) RES 341 Week...

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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 experienced Swiss watch maker Jean Dubois to head the Mechanical Watches Division. We have an aggressive advertisement campaign with race car driver Kyrsten Nieman which recent surveys have shown is attracting customers. Aquine watches have consistently received high marks in four of the seven tests administered by the Swiss Official Chronometer Control. Aquine is ready to make several investments which will move it from the role of the “new comer” to the Chronometer market to an established competitor. The Swiss Official Chronometer Control (SOCC) is the only agency which can give a watch the coveted “Chronometer” label. The SOCC rejected sixty seven percent (67%) of Aquine watches submitted for “Chronometer” certification. This figure is up from fifty four percent (54%) last year and up from thirty two percent (32%) in the first year Aquine first submitted watches for “Chronometer” certification. The three tests which Aquine watches are consistently failing at SOCC......

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...Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur Module No. #01 Lecture No. #07 Random Variables So, far we were 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 card in a drain probability of various kinds of events. However, in most of the practical situations we may not be interested in the full physical description of the sample space or the events; rather we may be interested in certain numerical characteristic of the event, consider suppose I have ten instruments and they are operating for a certain amount of time, now after amount after working for a certain amount of time, we may like to know that, how many of them are actually working in a proper way and how many of them are not working properly. Now, if there are ten instruments, it may happen that seven of them are working properly and three of them are not working properly, at this stage we may not be interested in knowing the positions, suppose we are saying one instrument, two instruments and so, on tenth...

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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 of many observations. These observations are called the outcomes of the experiment. The collection of all outcomes for an experiment is called a sample space. Table 1 Examples of Experiments, Outcomes, and Sample Spaces Experiment Outcomes Sample Space Toss a coin once Head, Tail S= { Head, Tail} Roll a die once 1, 2, 3, 4, 5, 6 S= {1, 2, 3, 4, 5, 6} Toss a coin twice HH, HT, TH, TT S= { HH, HT, TH, TT} Play lottery Win, Lose S= {Win, Lose} Take a test Pass, Fail S= {Pass, Fail} Select a worker Male, Female S= { Male, Female} 3 A random variable is a variable whose value is determined by the outcome of a random experiment. A random variable that assumes countable values is called a discrete random variable. A random variable that can assume any value contained in one or more intervals is called a continuous random variable. 4 2 7.10.2015 г. Examples of discrete random variables 1. The number of...

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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. This information will need to be studied by all department heads. Overview of the data set This data set of information contains information on the breakdown of the survey that was conducted on the company Use of statistics and probability in the real world Companies use statistics in the real world to get and have an advantage. They can be used for things such as knowing the latest stats on a sports figure or what items a consumer will likely buy from the local hardware store Distributions Distribution table contains the information that gives the breakdown of how the study was conducted and who the participants were in the study. This information is important to AIU for the company will be able to better prepare for the future when they know how to better manage their work force Then complete the following distribution tables. Please pay attention to whether you should present the results in terms of percentages or simple counts. Gender |Gender ......

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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, satisfaction of legal services, sentence satisfaction, and incarceration services satisfaction. This data-set was used to profile the satisfaction of future inmates. This email represents our analysis of the data for the same purpose using the concepts of probability. Before we address the results of the survey, we will discuss the importance of inmate satisfaction, the concept of probability, and the uses of probability in business. Research has shown that inmates who are satisfied with their incarceration are more cooperative. Therefore the number of incidents involving inmates are reduced. The term probability is a measure of the likelihood of a random phenomenon or chance behavior. Probability describes the long term proportion with which a certain outcome will occur in a specific situation with short term uncertainty. Probability deals with experiments that yield random short term results or outcomes but they reveal long term predictability. Perfect information is......

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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 and procedures with the results expanded in this memorandum. Investigation The current advertising campaign features a race car driver as ambassador of the brand who has been successful in the circuit with several wins as of late. This seems like an excellent choice because race enthusiasts like to keep time on their own for their favorite drivers. A couple of questionnaires were sent to consumers and to dealers with nominal, ratio, and interval sampling questions aimed at the effectiveness of the advertising strategy (Sekaran, 2003). The results on consumers were very positive with over sixty percent admiring the driver and considering purchasing an Aquine product because of the campaign and for dealers, while the results were more subdued at fifty percent for positive effect and eighteen percent for ineffective, the perception was also positive. The watch production is sent to a certification entity that is called the Swiss Official Chronometer Control (SOCC) and the rejection......

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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 reduced budgets. Introduction These are the cuts that are recommended to keep the clinic functioning in a manner that they can keep up with rising demand for their services. In this scenario the majority of cost cuts were non employee wages. Advertising, custodial, security, and supplies took most of the brunt of the cuts. If employees don’t mind doing most of the custodial duties during the times that they have nothing to do then that is a cost you can cut. If the clinic is doing well then advertising cost can be cut down because the best advertising is word of mouth which does not cost anything but good customer relations. Security could be important but in order not to effect the functions of the clinic you can get rid of security until you can afford it again. Purchasing supplies you can look at different ways in order to save money in getting supplies, such as purchasing them at a cheaper place, reusing things that can be reused and not buy anything new until you can......

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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 with the outcomes' relative likelihoods and distributions. In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics. There are several competing interpretations of the actual "meaning" of probabilities. Frequentists view probability simply as a measure of the frequency of outcomes (the more conventional interpretation), while Bayesians treat probability more subjectively as a statistical procedure that endeavors to estimate parameters of an underlying distribution based on the observed distribution. The conditional probability of an event A assuming that B has occurred, denoted ,equals The two faces of probability introduces a central ambiguity which has been around for 350 years and still leads to disagreements about...

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