...quantities are called operational quantities. The laws which relate operational quantities are called operational laws. Operational laws for computer systems will be studied in this note. We …rst introduce some notation. Notation: M =Number of queueing centers in the network. T = Finite observation period. Ai = Number of arrivals at queue i (device i) during observation period. Bi = Total busy period of queue i during observation period. Ci = Number of service completions at queue i during observation period. Di = Total service demand by a customer at device i. Qi = Queue length at device i (including the job in service) Ri = Response time per visit to the ith device. Si = Average service time per customer visit to queue i during observation period. Ui = Utilization of queue i during observation period. Vi = Average number of visits to queue i by a customer before it leaves the system during observation period. Xi = Throughput of queue i during observation period. i = Arrival rate of queue i during observation period. pij = The transition probability of a job moving to the jth queue after service completion at the ith queue. The following variables correspond to the entire system under observation. D = Sum of service demands on all devices. Dmax = Service demand on the bottleneck device....
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...Name-------------------------- School------------------------------------------------------------- Age: -------------------------- Class------------------------------- SECTION B Process of Science Test (PST) 1. | Which science process skill involves using your five senses to describe what is seen, heard, felt, smelt, and tasted? | | | A. | Inferring | B. | Predicting | C. | Measuring | D. | Observing | 2. | Which science process skill is an explanation of observations? | | | A. | Inferring | B. | Predicting | C. | Measuring | D. | Observing | 3. | Which science process skill is used mostly in experiments and is in the form of an If...then statement? It is a statement that can be proven as true or false. | | | 4. | Which science process skill uses numbers to describe an object? | | | A. | Inferring | B. | Predicting | C. | Experimenting | D. | Measuring | | | 5. | Which science process skill involves making up categories or grouping things together? | | | A. | Experimenting | B. | Measuring | C. | Classifying | D. | Analyzing Data | 6. | Which science process skill uses a test under controlled conditions? | | | A. | Measuring | B. | Experimenting | C. | Collecting Information | D. | Inferring | 7. | Which science process skill involves sharing ideas through talking and listening, drawing and...
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...probability. If A and B are disjoint, P(A or B)= P(A) + P(B) General addition rule- P(A or B) = P(A) + P(B) – P(A and B) If A and B independent- P(A and B) = P(A) * P(B) Discrete RV- takes on one of a list of possible values Continuous RV- takes on any value in an interval Volatility drag = ½ (annual variance) Long-run return= expected annual return – volatility drag OR expected annual return – (annual variance)/2 Z-score = X - mean/SD Bernoulli Requirements • Two possible outcomes • Fixed probability of success • Independence Binomial requirements- model for categorical variables • Total number of observations, n, is fixed • The outcomes of all observations are independent • Each observation falls into just one of 2 categories • All observations have the same probability of success It is okay to ignore dependence if the trials make up less than 10% of the population P hat is a statistic – p(hat)= X/n Bernoulli Distribution- simulates one sample and see the individual successes and failures Binominal Distribution- simulates several samples and see the number of successes and failures in each sample Sampling error- the difference between sample proportions and the true proportion. This is the sample variability from one sample to the next. Data AVERAGE STDEV.S Discrete random variables X1p1+ xnpn Sqrt(var) Bern Sum P Sqrt(pq) Binomial, X is # successes in n trials Sum N*p Sqrt(np*q) Sample proportion p(hat)=X/n Sum P(hat) Sqrt(pq/n) Sample mean...
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...Statistics Chapter 2 Methods for Describing Sets of Data Quantitative data is information about quantities; that is, information that can be measured and written down with numbers. Qualitative data is information about qualities; information that can't actually be measured. A class is one of the categories into which qualitative data can be classified. The class frequency is the number of observations in the data set that fall into a particular class. The class relative frequency is the class frequency divided by the total number of observations in the data set; that is, class relative frequency = (class frequency) / n. The class percentage is the class relative frequency multiplied by 100; that is, class percentage = (class relative frequency) x 100. Summary of Graphical Descriptive Methods for Qualitative Data Bar Graph: The categories (classes) of the qualitative variable are represented by bars, where the height of each bar is either the class frequency, the class relative frequency, or the class percentage. Pie Chart: The categories (classes) of the qualitative variable are represented by slices of a pie (circle). The size of each slice is proportional to the class relative frequency. Pareto Diagram: A bar graph with the categories (classes) of the qualitative variable (i.e. the bars) arranged by height in descending order from left to right. Summary of Graphical Descriptive Methods for Quantitative Data Dot Plot: The numerical value of each quantitative...
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...Quality Control Simon Shaw s.c.shaw@maths.bath.ac.uk 2005/06 Semester II 1 Introduction In quality control, we are concerned with problems involved in controlling the quality of a manufactured product. We’ll study two major techniques: 1. ACCEPTANCE SAMPLING where we are concerned with monitoring the quality of manufactured items supplied by the manufacturer to consumers in batches. The problem is to decide whether the batch should be accepted or rejected on the basis of a sample randomly drawn from the batch. 2. PROCESS CONTROL where goods are produced continuously and the problem is to detect changes in the performance of the manufacturing process and take action (when necessary) to control the process. 1.1 What is quality? Most of us associate quality with luxury (such as a BMW car, a plasma screen television, . . . ) but by quality control we are thinking in terms of “things that work in the way we expect them to” i.e. “it does what it says on the tin”. 1. Quality implies fitness for use. 2. Quality means conformance to requirements. Thus, quality is defined by both customers and producers. 1.2 Variability compromises quality Mass produced items are not identical. Some variation is inevitable and can cause problems. Too much variation might mean that parts which should fit together don’t. e.g. A screw might be too small/large to fit the corresponding bolt. There is a need to identify items which exhibit too much variation and deal with them, perhaps...
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...where E[ε|X] = 0, E[εε |X] = σ 2 I n ; and X includes an intercept term. You do not observe the data set Z = [y X]. Instead you observe 150 15 50 Z Z = 15 25 0 50 0 100 2 Compute the least squares estimators β, s2 , R2 and RAdj (the adjusted R2 ). Is there anything to be gained by observing the full data set? 2. Suppose you have the simple regression model with no intercept: yi = xi β+ i for i = 1, 2. Suppose further that the true value of β is 1, the values of xi observed in the sample are x1 = 2 and x2 = 3, and the distribution of i is Pr( i = −2) = Pr( i = 2) = 1/2 with 1 independent of 2 . (a) Find the least squares estimator of β. (b) What is it mean and variance? Is it BLUE? (c) Consider the alternative estimator β ∗ = y /¯, where y is the sample mean ¯ x ¯ of yi and x is the sample mean of xi . What is the mean and variance of ¯ β ∗ ? Is it unbiased? (d) Which estimator is more efficient, the least squares estimator or β ∗ ? 3. Suppose x1 , x2 . . . xn is an independent but not identically distributed random sample from a population with E[xi ] = µ and Var[xi ] = σ 2 /i for i = 1, 2, . . . , n. Consider the following class of estimators for the population mean µ: n µ= ˆ ci xi where c1 , . . . , c n are constants i=1 Each sequence {c1 , c2 , . . . , cn } defines an estimator for µ. (a) Give a necessary and sufficient condition on the ci for µ to be an unbiased ˆ estimator of µ. (b) Find the best unbiased estimator...
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...qualitative research, the researcher is usually: a. Trying to test existing theory b. Looking to create new theory during and after the research c. Testing fixed relationships between variables d. Looking at a very large number of data points Answer 2. Qualitative research looks for _______, while quantitative research looks for _________ a. Quality, Quantity b. Quantity, Quality c. When, Why d. Meaning, Measurement Answer 3. The person who “sets the tone” for a focus group is: a. The Moderator b. The Dominator "c. The Cynic " d. The Co-Moderator Answer "4. If a researcher is interested in documenting a particular event to gain insight on the specific processes and dynamics of that event, the researcher is likely to conduct a(n):" a. Observation Survey b. Survey c. Case Study d. Triangulation Study Answer 5. An important tool for extracting meaning from completed interview and focus group transcripts is: a: Cross-sectional surveys b. Content analysis c. Chronologic interviewing d. Extralinguistic sampling Answer...
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...Binomial Distributions How to recognize binomial random variable: 1. The sample size n is fixed. 2. The n observations (or trials) are independent. 3. There are only 2 possible outcomes for each observation. They are labeled “Success” and “Failure” 4. The probability of success is the same for each trial. Let p = success probability and 1 – p = failure probability 5. The binomial random variable is . . . X = the number of successes out of n observations. Binomial distributions are identified specifically by two parameters: n and p. X takes on values 0, 1, 2, . . . , n Notation: [pic] Mean: [pic] Variance: [pic] Standard deviation: [pic] The Binomial Probability Formula: [pic] Suppose [pic], then the probability of observing 16 successes out of 20 observations is [pic] Find the mean, variance, and standard deviation of X. Mean: [pic] Variance: [pic] Standard deviation: [pic] Table 3 in Appendix II contains probability distributions for a variety of binomial distributions. Look up the following probabilities: For X ~ B(20, 0.7), find P(X=16). Answer: P(X=16) = 0.130 For X ~ B(8, 0.45), find P(X > 5). Answer: P(X > 5) = P(6) + P(7) + P(8) = 0.070 + 0.016 + 0.002 = 0.088 More examples: 1. A research team found that 10% of...
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...Descriptive Statistics Descriptive statistics involves organizing, summarizing and illustrating statistical data. The objective is to show important characteristics of the data without drawing any conclusions. Inferential statistics involves using a representative subset of data (a sample) in order to draw conclusions about unknown characteristics of an entire set of data (a population). Population: The entire set of elements of interest (i.e. all humans, all working-age people in Canada, all IT companies). A population parameter is a characteristic used to describe a population. For example, Population mean ( Population standard deviation ( Population median ( The values of the population parameters would be preferable for use in decision-making but seldom will these values be known since collecting all the population elements (a census) is usually too expensive and/or time consuming. Sample: A representative subset of the entire set of elements of interest that is used to gain insight about the population. A sample statistic is a characteristic used to describe a sample. For example, Sample mean [pic] Sample standard deviation s Sample median Md It is cheaper, less time-consuming and more practical to use sample statistics as estimates for population parameters in making business decisions. How well the sample represents the population depends on...
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...with multiple problems can benefit from the treatment of a clinical psychologist. This is true because the clinical psychologist can offer different forms of treatments for the many problems one person can face. This paper will discuss the field of clinical psychology, the history, research methods, and the differences in different fields of psychology. Clinical Psychology Clinical psychology is a science (Plante, 2010). This is true because it uses scientific methods to uncover and validate information. This information includes what kind of behavior and personality people have, and what causes a person to develop (emotions, thinking, and behavior). Clinical psychologists can practice in his or her field in a variety of ways (Irving B. Weiner, n.d.). Some...
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...that the person actually has the condition? (Note that this is presumably not the same as the simple probability that a random person has the condition, which is 1 just 20 .) This is an example of a conditional probability: we are interested in the probability that a person has the condition (event A) given that he/she tests positive (event B). Let’s write this as Pr[A|B]. How should we define Pr[A|B]? Well, since event B is guaranteed to happen, we should look not at the whole sample space Ω , but at the smaller sample space consisting only of the sample points in B. What should the conditional probabilities of these sample points be? If they all simply inherit their probabilities from Ω , then the sum of these probabilities will be ∑ω ∈B Pr[ω ] = Pr[B], which in general is less than 1. So 1 we should normalize the probability of each sample point by Pr[B] . I.e., for each sample point ω ∈ B, the new probability becomes Pr[ω ] Pr[ω |B] = . Pr[B] Now it is clear how to define Pr[A|B]: namely, we just sum up these normalized probabilities over all sample points that lie in both A and B: Pr[A|B] := ∑ ω ∈A∩B Pr[ω |B] = Pr[ω ]...
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...Pergamon English for SpecificPurposes, Vol. 16, No. 2, pp. 119-138, 1997 © 1997 The AmericanUniversity.Published by ElsevierScience Ltd All rights reserved. Printed in Great Britain 08894906/97 $17.00+0.00 PIh S0889-4906(90)00019-1 T h e M e d i c a l R e s e a r c h Paper: S t r u c t u r e and Functions K evin Ngozi N w o g u A bstract--Studies i nto the organization of information in the medical research p aper have tended to present accounts of the structure of information in s ections in isolation. The structure of information in all sections of the medical r esearch paper was investigated using Swales' (1981, 1990) genre-analysis m odel. An eleven-move schema was identified, out of which nine were found t o be "normally required" and two "optional". Each schema was found to e mbody "constituent elements" and to be characterized by distinct linguistic f eatures. The study provides insights into the nature of discourse organization in this genre of written discourse. © 1997 The American University. Published b y Elsevier Science Ltd I ntroduction A s with most experimental research reports, the medical research paper is a highly technical form with a standard format for the presentation of i nformation. This format is the division of the paper into "Introduction, M ethods, Results and Discussion" - - the traditional IMRD sections of the r esearch paper. M ost research article writers are familiar with the IMRD format, but not all are conscious...
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...of the following except: A) The median of each of the variables. B) The range of each of the variables. C) An indication of outliers. D) Patterns of values. ANSWER: A 2. For the following scatter plot, what would be your best estimate of the correlation coefficient? A) -0.8 B) -1.0 C) -0.3 D) 0.0 ANSWER: A 3. For the following scatter plot, what would be your best estimate of the correlation coefficient? A) 1.0 B) 0.8 C) 0.3 D) 0.0 ANSWER: B 4. Calculate the correlation for the following (X, Y) data: (53, 37), (34, 26), (10, 29), (63, 55), (28, 36), (58, 48), (28, 41), (50, 42), (39, 21), and (35, 46). A) 0.710 B) 100.6 C) 0.670 D) 0.590 ANSWER: D 5. Suppose that we are interested in exploring the determinants of successful high schools. One possible measure of success might be the percentage of students who go on to college. The teachers’ union argues that there should be a relationship between the average teachers’ salary and high school success. The following equation of the regression line is obtained: “% of students going on to college = 13 + 0.001Average Teachers’ Salary” Which of the following statements is true? A) Increase % of students going on to college by 0.001 percent, we would expect average teacher’s salary to increase by one dollar. B) Increase % of students going on to college by one percent, we would expect...
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...given value of X, a estimates the intercept of the regression line with the Y axis, and b estimates the slope or rate of change in Y for a unit change in X. Y! The regression coefficients, a and b, are calculated from a set of paired values of X and Y. The problem of determining the best values of a and b involves the principle of least squares. 10.1 The Regression Equation To illustrate the principle, we will use the artificial data presented as a scatter diagram in Figure 10-1. Figure 10-1. A scatter diagram to illustrate the linear relationship between 2 variables. Because of the existence of experimental errors, the observations (Y) made for a given set of independent values (X) will not permit the calculation of a single straight line that will go through all the points. The least squares line is the line that goes through the points so that the sum of the squares of the vertical deviations of the points from the line is minimal. Those with a knowledge of calculus should recognize that this is a problem of finding the minimum value of a function. That is, set the first derivatives of the regression equation with respect to a and b to zero and solve for a and b. This procedure yields the following formulas for a and b based on k pairs of X and Y: If X is not a random variable, the coefficients so obtained are the best linear unbiased estimates of the true parameters. b X X Y Y X X XY X Y k X X k a X Y X XY X X k Y bX ! " " " ! " " !...
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...BARTHÉLEMY CABOUAT THIBAULT MATHIEU ENCADRÉS PAR JEAN-MARC BARDET MAI 2014 Travail d’étude et de recherche : Les chaînes de Markov cachées Table des matières Introduction 2 Présentation générale 3 Chaînes de Markov 3 Propriété de Markov 3 Homogénéité 4 Noyaux de transition 5 Modèle de Markov caché 5 Définition 5 Exemple 7 Propriétés 9 Inférence 12 Estimateurs de paramètres : les MLE 12 Probabilité d’une séquence d’observations : l’algorithme Forward-Backward 15 Algorithme de Viterbi 17 Notations 17 Principe 18 Applications 20 Simulations Matlab 20 Inférence paramétrique 20 Algorithme de Viterbi 24 Application à la domotique 26 Conclusion 31 Bibliographie 32 Introduction Les modèles de Markov cachés ont été introduits par Baum et son équipe dans les années 60. Ils sont apparentés aux automates probabilistes, c’est-à-dire définis par une structure composée d’états et de transitions ainsi que par un ensemble de distributions de probabilité sur ces transitions. Les chaînes de Markov cachées sont utilisées dans différents cadres, que ce soit au niveau des objectifs visés ou bien des espaces considérés (discrets, continus). Les applications en sont nombreuses dans des domaines tels que le traitement du signal, la reconnaissance de la parole, le text mining (filtrage de spam, reconnaissance de parties de discours), la finance de marché, la bio-informatique, la physique quantique... Notre objectif est de proposer une vue d’ensemble de la...
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