firms to the market, total transactions costs **for** the economy are minimized. d. The **limit** of the firm varies over time: technological /the problem and also draws upon known mathematical **theorems** to aid in reasoning. The major difference between/reported “critical value”). **Dummy** Variable Technique… - Multiple regression can be used to analyze the effects of qualitative variables. - **Dummy** variable = a / and invention; but destroys as well. 12.**Centralized** government…boosted in post-WWII Germany and Japan /

that supplies the samples doesn’t have to be a normal distribution **for** the **Central** **Limit** **Theorem** to hold. What if the population is a normal distribution? In that case, the sampling distribution of the mean is a normal distribution regardless of the sample size. J. Schmuller, Statistical Analysis with Excel **For** **Dummies** The **limits** of confidence Sampling distributions help you to answer the question: How much/

) is not constant, the usual t statistics and confidence intervals are invalid no matter how large the sample size is; the **central** **limit** **theorem** does not bail us out when it comes to heteroskedasticity. is a consistent estimator of 4.2 TESTING HYPOTHESES: A Single Population/ (and the same error term u). Intercept Shift **Dummy** Variable Trap: to keep track of which group is the base (benchmark) group. we will always include an overall intercept **for** the base group. Nothing changes about the mechanics of OLS/

is Represented by Node as the Completion of an Activity Arrows Represent the Sequential Linkages Between Activities **For** Example, Node 1 is Begin, Node 2 is Complete Task 1, Node 3 is Complete /3 Correct 1-2 2-4 4-5 1 2 4 5 2-3 3 3-4: **Dummy** activity Network Diagramming First Step in Project Management Begins with a Work Breakdown Lists the “WHAT’/ Estimate = Sigmae te = (a + 4m + b)/6 Sigmae = (b - a)/6 Can Use **Central** **Limit** **Theorem** to Estimate Project Time Example Network Flow Diagram 7 6 5 4 3 2 1 A G C I H /

distribution would start to look like the theoretical probability distribution. **For** an infinite number of experiments, the frequency and probability distributions would be identical. Significance of Sample Size **Central** **Limit** **Theorem**: the larger the sample size, the greater the probability that/others would get a zero on the variable. Let’s create a **dummy** variable **for** the variable “Country of origin” in the Cars.sav data set. The new **dummy** variable will be “American in Origin.” If you look at the country/

**Theorem** Consider annuli shapes A(r) of inner radius r, unit area, and critical density **For** all, there exists a finite, such that A(r*) percolates, **for** all It is possible to decrease the percolation threshold by taking a sufficiently large shift ! CNP Squishing and squashing Shifting and squeezing What have we proven? CNP Among all convex shapes the hardest to percolate is **centrally**/**dummy**” observation when then take the **limit** **for** t =0 Derive Kalman equations using a **dummy** observation Then take the **limit** **for**/

**for** probabilistic cost analysis Identify sources of cost variance and separate deterministic effects Identify correlated random effects and estimate their standard deviations (not to be added quadratically!) Estimate mean value and standard deviation of independant elementary costs and modelize by simple skew law, e.g. exponential Apply **central**-**limit** **theorem**/ test … **dummy** data sets links CLIC-ILC Cost & Schedule 16 http://www-ilcdcb.fnal.gov/example_26march09-Construction.xls Use EDMS **for** archive, approval/

in the variance formula; Estimation of the variance gives another minor correction: T n-1 instead of Z critical and p-values) The **central** **limit** **theorem** does not apply since we are concerned with the distribution of Y 0, not the distribution of The Distribution of (Y 0 - /statistic is Z = t i /(g 1/2 s t ), where t i is the t-statistic from the univariate **dummy**-variable-based regression model **for** firm i, and s t is the sample standard deviation of the g t-statistics. Algorithm: (i) create a pseudo-/

1 2 3 a b Operations Research II Course,, September 201329 EXAMPLES OF THE USE OF DUMMYACTIVITY **Dummy** RIGHT 1 1 2 Activity c not required **for** e a b c d e a b c d e WRONG !!! RIGHT Network concurrent activities/activities. The project variance is the sum of the variances of the critical path activities. The expected project time is assumed to be normally distributed (based on **central** **limit** **theorem**). In example, expected project time (t p ) and variance (v p ) interpreted as the mean ( ) and variance ( 2 )/

k y,k z volume kXkX kZkZ Fourier slice **theorem** in tomography (Kak, Computer Aided Tomography, 1988) / Tip-Tilt at altitude → Dynamic Plate Scale changes Credit: Rigaut, MCAO **for** **Dummies** Page 17 Outline of lecture Review of AO tomography concepts AO applications of /modest correction over a very wide field of view **Central** parts of the globular cluster Omega Centauri, as/ can take advantage of smaller image –Potential improved SNR **for** background-**limited** point sources Page 56 Credit: A. Tokovinin time Page/

measures Income time **dummies**, other locational **dummies** Examine findings Updated /**central** core less attractive as costs of land increase lowers Office Bid Rent Reduces employment density R u R Office R residential R ag. Service **limit** Your book looks at other examples of these effects You are responsible **for**/**limited** controls. Consequences More multifamily housing. Smaller lot sizes in some areas. Industrial and commercial activities separated. More strip malls. Neighborhood covenants used Coase **Theorem**/

us that the sample mean will converge to the population (true) mean as the sample size increases. **Central** **Limit** **Theorem** **Central** **Limit** **Theorem** tells us that **for** many samples of like and sufficiently large size, the histogram of these sample means will appear to be /true? Produce descriptive statistics labour comparing the two groups Produce a group variables which equals 1 **for** US firms, 0 otherwise This is called a **dummy** variable Write out H 0 and H 1 Analyse Comparer les moyennes Test t /

random variable is distributed as Student ’ s t with (n – k - 1) degrees of freedom. In addition the **central** **limit** **theorem** enables us to conclude that this result is approximately valid **for** a wide range of non-normal distributions and large sample sizes, n. t= (b j – j ) / / )/Y 1 ) ≈ (Y 2 -Y 1 )/Y 1 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson11-78 **Dummy** Variables A **dummy** variable is a categorical independent variable with two levels: yes or no, on or off, male or female recorded as 0 or 1/

a 46 percent error in one simulation! Average MWTP is a **limited** concept, even with the correct specification; it cannot be compared across/ parametric forms **for** a hedonic as special cases. It allows **for** household heterogeneity. It leads to tests of key sorting **theorems**. My Envelope/ 0.1414***0.0067 Air Cond.House has **central** air conditioning 0.0254***0.0055 FireplacesNumber of fireplaces/2(Minority Teachers 1) squared- 0.7161*0.3921 Cleveland SD **Dummy** **for** Cleveland & E. Cleveland Schl. Dists. 0.47550.3269 Near/

max LT(i) min 100 299 399 416 526 638 Example 6: 1 65 4 2 3 A 6 B 9 **Dummy** C 8 D 7 E 10 F 12 54 **For** an arbitrary arc representing activity (i,j), the Fotal Float (TF), represented by TF(i,j), of the activity/on a critical path found by CPM. PERT assumes that the critical path found by CPM contains enough activities to allow us to invoke the **Central** **Limit** **Theorem** and conclude that the following is normally distributed: : expected duration of activities on any path : variance of duration of activities on any /

not appropriate because it rules out sorting. Average MWTP is a **limited** concept, even with the correct specification; it cannot be compared/parametric forms **for** a hedonic as special cases. It allows **for** household heterogeneity. It leads to tests of key sorting **theorems**. Estimates / 0.1414***0.0067 Air Cond.House has **central** air conditioning 0.0254***0.0055 FireplacesNumber of fireplaces/2(Minority Teachers 1) squared- 0.7161*0.3921 Cleveland SD **Dummy** **for** Cleveland & E. Cleveland Schl. Dists. 0.47550.3269 Near/

measurement of political representativeness DROUGHT-captures environmental effects PROPERTY, COMMAID-**dummy** **for** 2 types of property rights regimes over elephants in Africa /**central** planner—what if we relax this assumption? Pigovian taxes can “break” Coase **Theorem** Factory imposes costs on houses of $60 K per year. Govt imposes Pigovian taxes of $60K Factory can install soundproofing **for**/“captured” Quotas Quotas are a method of setting allowable **limits** on output or the usage of externality creating inputs. /

replays the same question one time. Corollary 1: Similar to **theorem** 2, an intruder can found the window W in expected trials/ NCYU, Taiwan, R.O.C.38 Confirmer Signatures with **Limited** Verifiers Malicious confirmer The confirmer may prove the correctness of the/ NCYU, Taiwan, R.O.C.55 Honeypot Honeypot uses the **dummy** or virtual environment (i.e. a true system of low security/ The **centralization** recording work, in RMS host, will not influence the general host system on efficiency and is good **for** system managers/

regardless of the form of the underlying distribution of the population, provided that the sample size is large enough. **Central** **Limit** **Theorem** tells us that **for** many samples of like and sufficiently large size, the histogram of these sample means will appear to be a normal / true? Produce descriptive statistics labour comparing the two groups Produce a group variables which equals 1 **for** US firms, 0 otherwise This is called a **dummy** variable Write out H 0 and H 1 Run the student t test What do you/

Irreducibility **Theorem** [Chandra, Hadzilacos, Jayanti, Toueg] **Theorem**: **For** /on each port is **limited** to a designated “/ to the **centralized** simulation. –/**For** every port i, one i-perform task, one i-output task. Explicitly program fault-tolerance: –Keep track of which ports have failed. –When > f failures have occurred, the object need not respond to anyone (but it might). –When f failures have occurred, the object must respond to every invocation on a non-failing port. –Convention: Each i-task includes a **dummy**/

and The second expression may be written as which is known as Bayes **theorem**, so named after the 18th century mathematician Thomas Bayes. Digital Image Processing,/**For** example, the second, third, and fourth **central** moments are intimately related to the shape of the probability density function of a random variable. The second **central** moment (the **centralized**/the integral operator between the **limits** and x. Then, the output in terms of the input is given by where w is a **dummy** variable of integration. This /

b a c e 1 2 5 6 d 4 **DUMMIES** **FOR** UNIQUENESS OF ACTIVITY REPRESENTATION EXAMPLE 5 S T **DUMMIES** **FOR** CREATION OF A SINGLE SOURCE AND SINK THE ROLE OF **DUMMIES** IN PROJECT NETWORKS Role of **Dummy** I II III Network type A-O-A yes yes/STANDARD PERT ASSUMPTIONS 1. The activities are independent 2 The critical path contains a large no. of activities so that we can invoke the **Central** **Limit** **Theorem**. 3 .All activities not on the critical path are ignored. 4. Activity times follow a Beta distribution. 5. The mean and /

PERT DIAGRAMMING (**DUMMY** ACTIVITIES) Uses 1. Clarify Precedence A C A B **Dummy** B OK D C D OK, but different meaning PERT DIAGRAMMING (**DUMMY** ACTIVITIES) Uses 2. Clarify Event Numbers A A C B B **Dummy** Not correct, OK in concept C PERT DIAGRAMMING (**DUMMY** ACTIVITIES) Uses /10 9 5 G 11 J B H D 8 61 3 E 7 Network Paths **for** the St. Adolf’s Hospital Project PROBABILITY OF MEETING THE PROJECT DUE DATE The **central** **limit** **theorem** allows us to use the normal probability distribution to find the probability of achieving a /

is widely used. Part of its appeal is that it is well behaved and mathematically tractable. **Central** **limit** **theorem** Sample variance and standard error Variance of the sample mean of an SRS of ‘n’ units **for** a population of size ‘N’: e = standard error Measure of sampling error./Unknown, but can be estimated without bias by: Proportions A proportion P (or prevalence) is equal to the mean of a **dummy** variable. In this case Var(P) = P(1-P), and It is not sufficient to simple report the sample proportion/

synchronization, **dummy**, access Format of a burst defied by its function DL: normal, frequency correction, synchronization, **dummy** UL: normal, access Time/Frequency/Amplitude diagram **for** GSM normal/**central** frequency of the carrier Only on the forward link Spectral characteristics of the control channel. The peak in the spectrum allows **for**/ Page 37 Sampling and Quantization Sampling oSampling **theorem** specifies conditions **for** discretization of band **limited** analog signals oVoice needs to be sampled at /

, known generalities about properties: Use bootstrapping Root N consistency Sampling conditions amenable to **central** **limit** **theorems** Compute by resampling mechanism within the sample. Bootstrapping Method: 1. Estimate parameters using/unobservables) Approaches (Parametric) Control Function: Build a structural model **for** the two variables (Heckman) (Semiparametric) Instrumental Variable: Create an instrumental variable **for** the **dummy** variable (Barnow/Cain/ Goldberger, Angrist, current generation of researchers)/

way **Central** **limit** **theorem**: the magic of normally distributed sample means 14 Module 3 Correlation: causality from content, not statistics Linear regression: standard ordinary least squares (OLS) Error term: model change and transformations **for** ideal characteristics/of missing data, no need in statistical software If at all, then **for** all variables equally (**for** cross-variable relations) Expansion of the data set (additional variables, often **dummies**) Beware of implicit assumptions (A + B = Total: maybe there/

2012. Can cope with less data by making certain modeling assumptions. 77 Regression Discontinuity (RD) Future performance Coarsend test score **Dummy** Var: received schoolarship or not 78 RD Robustness Checks –Can individuals control if they are above or below the threshold? –/higher? Av(T) = 45.25 vs. Av(C) = 38.00 Is this significant? t-test assumes that Av(*) is normally distributed **Central** **Limit** **Theorem** holds **for** “large n” Small n: Fisher’s Exact Test Observed: Av(T) – Av(C) = 7.25 Permutation 1: Av(T) – /

values follow, the sample mean will follow a Normal distribution if the sample size is large.” **Central** **Limit** **Theorem**: Sample Size How large must n be **for** the CLT to hold? depends on how far the population distribution is from Normal the further from/ from a normal distribution No explanatory variable is an exact linear function of other explanatory variables (important with **dummy** variables) Interpretation of the Regression Coefficients The value of the dependent variable will change by j units with/

**central** tendency, measures of dispersion, measures of association, histogram, frequency tables, scatter plot, quantile Theory of probability: probability and its properties, random variables and distribution functions in one and in several dimensions, moments, convergence of random variables, **limit** **theorems**/ 3294 individuals (1569 females) Average wage p.h.: 6,31$ **for** males, 5,15$ **for** females Model: wage i = β 1 + β 2 male i + ε i male I : male **dummy**, has value 1 if individual is male, otherwise value 0 OLS /

but we could instead use AgeGroup, with several levels; e.g., child, adult, elderly. Stats packages turn each level into a **dummy** variable with values of 0 and 1, then treat each as a numeric variable. Example: Strength = a + b*AgeGroup is /to have values that come from a normal (bell-shaped) distribution. This assumption can be violated. Testing **for** normality is silly. The **Central** **Limit** **Theorem** assures a normal sampling distribution. With a count as the dependent, the error has a Poisson distribution, which/

**for** some unobservable factors, but may also introduce problems. Problems with Fixed Effects They all **limit** the variation in the data **for** estimating capitalization. School district fixed effects, **for**/**for** a hedonic as special cases. It allows **for** household heterogeneity. It leads to tests of key sorting **theorems**/ Air Cond.House has **central** air conditioning 0.0254***0/ Cleveland SD **Dummy** **for** Cleveland & E. Cleveland School Districts 0.14140.2232 Table 5A. Specification Tests and Results **for** Key School Variables/

robust, elegance n Disadvantages u Modeling **limitations**, correctness, realism Multiagents: Formal and/ they have duration. Situation Shortcomings: **central** decision making Multiagents: Formal and Economic 3/acting Laws, Norms, Conventions, Commitments Motivations **for** team formation: Shortcomings in ability Efficiency Failure/&Braynov Example (cont.) n Revenue equivalence **theorem** [William Vickrey, 1961]: The first- / discern the original function. n Using **dummy** items and functions. n Watermarks and /

05B 714 7 07D 79 1315 62C 1416 14 16 02F 910 1516 61E **Dummy** Time Management ESEF LSLF SlackDur. Act Key Activity-on-node network 5/18/ K. Gaafar Important Distributions 5/18/2015 L. K. Gaafar Stochastic Times The **Central** **Limit** **Theorem** The sum of n mutually independent random variables is well-approximated by a normal distribution/DC 5712 EATriangular336 FA, BTriangular588 GE, DUniform9NA9 Construct an activity-on-arrow network **for** the project above. Provide a 95% confidence interval on the completion time of /

path found by CPM contains enough activities to allow us to invoke the **Central** **Limit** **Theorem** and conclude that the following is normally distributed: Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc. 42 a, b and m **for** activities in Widgetco Activityabm (1,2)5139 (1,3)2106 (3,5/ slide: Copyright © 2004 Brooks/Cole, a division of Thomson Learning, Inc. 44 Of course, the fact that arc (2,3) is a **dummy** arc yields E(T 23 )=varT 23 =0 The critical path was 1-2-3-4-5-6. Thus, E(CP)=9+0+7+10/

k () may be any function of data. Examples: Logs and levels in economics Time trends, and time trends in loglinear models – rates of growth **Dummy** variables Quadratics, power functions, log-quadratic, trig functions, interactions and so on. 78/97 Linearity Simple linear model, E[y|x] =x’β / Observations are independent Assumption will be unnecessary – we will use the **central** **limit** **theorem** **for** the statistical results we need. 89/97 The Linear Model y = X +ε, N observations, K columns in X, /

Dependency Continuity Outline Contd.. **Dummy** activities Numbering Efficiency Procedures **for** drawing the network Activity list Dependency Redundancy Approaches Homework Assignment 3 Rules **for** Diagramming Representation of activity. Representation /PERT) Outline: CPM vs PERT Advantages of PERT Statistics Review **Central** Tendency Dispersion Probability Distribution Function **Central** **Limit** **Theorem** Outline Cont: PERT Assumptions Activity Assumption Network Assumptions Example Homework /

path found by CPM contains enough activities to allow us to invoke the **Central** **Limit** **Theorem** and conclude that the following is normally distributed: Copyright © 2003 Brooks/Cole, a division of Thomson Learning, Inc. 46 a, b and m **for** activities in Widgetco Activityabm (1,2)5139 (1,3)2106 (3,5/ slide: Copyright © 2003 Brooks/Cole, a division of Thomson Learning, Inc. 48 Of course, the fact that arc (2,3) is a **dummy** arc yields E(T 23 )=varT 23 =0 The critical path was 1-2-3-4-5-6. Thus, E(CP)=9+0+7+10/

Topic 3 Outline Contd.. **Dummy** activities Numbering Efficiency Procedures **for** drawing the network Activity list Dependency Redundancy Approaches Example Homework Assignment # 3 CEM-510- Topic 3 Topic 4: Precedence Diagramming Outline: Rules **for** Diagramming Representation of activity. / Outline: CPM vs. PERT Statistics Review: **Central** Tendency and Dispersion Probability Distribution Functions **Central** **Limit** **Theorem** PERT Assumptions Activity Assumptions Network Assumptions PERT Computations Examples.

the same time (concurrently). A **dummy** activity shows a precedence relationship but reflects no passage of time. Two or more activities cannot share the same start and end nodes. Expanded Network **for** Building a House Showing Concurrent Activities/ is the sum of the variances of the critical path activities. The expected project time is assumed to be normally distributed (based on **central** **limit** **theorem**). In example, expected project time (t p ) and variance (v p ) interpreted as the mean ( ) and variance /

Network Concurrent Activities Figure 8. 6 Concurrent activities **for** house-building project 8-21 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■A **dummy** activity shows a precedence relationship but reflects no passage/ variance is the sum of the critical path activities’ variances ■The expected project time is assumed to be normally distributed (based on **central** **limit** **theorem**). ■In example, expected project time (t p ) and variance (v p ) interpreted as the mean ( ) and variance/

IF: Then Will have the form required so that there is a meaningful translation operator. In the **limit** of large N, the plane wave can have any wavelength. This is a symmetry argument… nothing much/to make the middle term a sum over k’. (It’s a **dummy** variable anyway.) Then the middle term has the same exponent (ikx) if k’+G = k i/ we can get a good answer with only a few terms in the **central** equation **for** the lower energy bands. Bloch **Theorem** Revisited. From the CE, the wavefunction is: u k (x) is /

**for** house-building project The Project Network **Dummy** Activities A **dummy** /**for** Windows Output Probabilistic Activity Times The Southern Textile Company Earliest and latest activity times Probabilistic Activity Times Expected Project Time and Variance Expected project time is the sum of the expected times of the critical path activities. Project variance is the sum of the critical path activities’ variances The expected project time is assumed to be normally distributed (based on **central** **limit** **theorem**/

differentiating factor is whether a student has completed a placement or not, then providing the sample sizes are large enough **for** the **central** **limit** **theorem** to apply, ANOVA, standard OLS regression, or indeed a simple comparison of means will provide a test of whether / simply the average final year mark and the primary interest is the coefficient **for** the placement **dummy** variable. **For** each sub-sample of students it is clear that going on placement improves performance, the variable is positive /

is most important **for** small samples; large samples are quite robust against this assumption because of the **central** **limit** **theorem** (averages are normally distributed even when the underlying trait is not!). 2. Homogeneity of variances **For** linear regression, the/does linear regression handle categorical predictors? Binary Treats the “0” and “1” as quantitative (numbers)! Categorical **Dummy** coding! Re-code the categorical predictor as a series of binary predictors! Binary variables Imagine that vitamin D was/

**central** mechanism Protects the server from overloads and performs encouragement. Virtual auction is Speak-Up’s main form of encouragement The thinner makes clients automatically send a congestion-controlled stream of **dummy**/ bot clients Unequal request/spoofing: charges clients **for** harder request when having an unequal request load. /B+G/c. Robustness to Cheating **Theorem**: “In a system with regular service intervals/ browser and it holds **dummy** data (1MB reflects some browsers **limits** on POSTs). The/

expected time to completion of the critical path is the sum of the mean activity times **for** the activities on the critical path. Strategic Project Management15SPM Basic PERT/CPM (Part 2) /,3) with variance of 2.78 y(3,4) with variance of 0.00 (**dummy**) y(4,5) with variance of 0.11 y(5,6) with variance of 0/ Basic PERT/CPM (Part 2) Probability Statements about Project Completion zFirst, we invoke the **Central** **Limit** **Theorem** y We will assume that the distribution of completion time is approximately Normal. yThis is /

DDoS Defense by Offense 8 Currency-based approach – Bandwidth **for** Currency **Central** mechanism – Thinner, Server front-end Thinner – Front-end/Cause client to send more traffic Proportional Reduction – Rate **limiting** Way to **limit** requests to server c requests/sec – Proportional Allocation/depends on application Approach II cannot claim that good clients get **Theorem** – If any client transmit ε fraction of average bandwidth it / Offense 30 Mean time to upload **dummy** bytes **for** good requests DDoS Defense by Offense/

Networks: Flow Without full network data, you can’t distinguish actors with **limited** information potential from those more deeply embedded in a setting. a b c/if removed from the group, would disconnect the group. Equivalently (by Menger’s **Theorem**): (b)A group’s structural cohesion is equal to the minimum number of/ the friends,etc. Structural indicators: Such as: **Centrality**, **dummies** **for** group / role membership, etc. These models are the only option **for** ego-network data,where information on network alters is/

merge and burst event. Are these rare or what? 17 **Dummy** activity ACADBDACADBD W R O N G 7 5 6 9 10 A B C D /minimum time subject to the precedence constraints. In addition, CPM provides: Starting and ending times **for** each activity Identification of the critical activities (i.e., the ones whose delay necessarily delay /4-5)6612711 G (5-6)612181242 H (6-7)36486048164 sum140 110 beta From the **Central** **Limit** **Theorem**, project completion time is normally distributed with a mean of 140 days and a standard deviation of/

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