...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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...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: Discrete...
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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 our...
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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 |Percentage...
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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 available...
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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 are...
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...Dear American Intellectual Union: I am writing to provide you with the job satisfaction statistics using gender, tenure, position, department, age, intrinsic and extrinsic data. Evaluating 44 people at random selection from those your organization offered. Some of this information will be in numbers and some in percentages to help give better understanding of the overall satisfaction of employees. The dataset used is from the surveys that ask several questions to give answers in order to help understand job satisfaction at a deeper level. There are many variables that have been used; there was gender, department, position, tenure and job statistic, by using quantitative and qualitative in addition to intrinsic and extrinsic data. For instance, the department of Human Resource Management for the State of Virginia received data on statistics of workplace conflict and found that difficulties in the workplace that step from troubled relationships accounts for 60 to 80 percent of those issues and that managers are spending one to two days weekly on trying to manage them. They also found that employees believe that discrimination is a large problem with in business and that in 2001; about 50 percent of employers reported they had been sued by employees. Another interesting find was that employers that used mediation or arbitration reduced litigation cost as much as 50 to 80 percent, but it still remains that the compensation amount for these type of suits have risen dramatically...
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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 afford...
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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 freedom...
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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 rate...
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...analysis using appropriate statistical methods allows the researchers to establish correlations between independent and dependent variables, define possible outcomes, and identify areas of potential study in the future accurately. Statistics is important for researchers because it allows them to investigate and interpret the data more accurately, and researchers will notice patterns in the data that would be overlooked otherwise and result in inaccurate and possibly subjective conclusions (Portney &ump; Watkins, 2009). Frequency distribution is a method used in descriptive statistics to arrange the values of one or multiple variables in a sample, so it will summarize the distribution of values in a sample. Frequency distribution is the most basic and frequently used method in statistics because it creates organized tables of data which can be used later to calculate averages or measure variability. The organized data frequency distribution provides continuous data that is easier to...
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...Section 4.1 Probability Distribution 1. Decide whether the random variable is discrete or continuous. (References: example 1 page 195, end of section exercises 13 – 20 page 201) (1 point per each part) a. The cost of a randomly selected apple continuous b. The height of randomly selected Statistics student continuous c. The number of books in the local college library discrete d. The braking time of a motorcycle continuous e. The number of cell phone call between Bagdad and Ft Bragg, NC on Christmas day in 2008 discrete 2. Decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property that is not satisfied. (References: example 3 and 4 page 197, end of section exercises 25 - 28 page 202 - 203) (5 points) |x |P(x) | |0 |0.49 | |1 |0.05 | |2 |0.32 | |3 |0.07 | |4 |0.07 | Yes, the distribution is a probability distribution because the probability of each value of the discrete random variable is between 0 and 1, inclusive. Also, the sum of all the probabilities is 1. 3. The table shows the probabilities associated with the number of defectives (x) in a group of four computers. Complete the table shown and find the mean, variance, and standard deviation for the distribution. Round b,...
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...Candidates A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. Full marks may be obtained for answers to ALL questions. This paper has seven questions. Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may gain no credit. 1. Explain briefly what you understand by (a) a sampling frame, (1) (b) a statistic. (2) 2. The continuous random variable X is uniformly distributed over the interval [–1, 4]. Find (a) P(X < 2.7), (1) (b) E(X), (2) (c) Var (X). (2) 3. Brad planted 25 seeds in his greenhouse. He has read in a gardening book that the probability of one of these seeds...
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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 x2...
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...analyses. Learning Objectives: Ser. # | Course Learning Objectives | Link with Program Learning Objectives | 1 | To understand the basic concepts and principles used in Business Statistics. | To inculcate business knowledge and analytical skills in graduates to think decisively in order to develop innovative solutions to problems in a business environment. | 2 | Organizing qualitative and quantitative data into a frequency table, displaying the data through charts and graphs, describing and exploring data through different numerical measures. | To provide a progressive and structured framework to graduates that enables them in developing and applying knowledge set of critical and ethical evaluation. | 3 | To know and understand probability and its different rules. | To craft graduates’ expertise in order to increase their resourcefulness. | 4 | To...
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