Psychology 282 Lecture #2 Outline. Review of Pearson correlation coefficient:

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Psychology 282 Lecture #2 Outline. Review of Pearson correlation coefficient:"

Transcription

1 Psychology 282 Lectue #2 Outline Review of Peason coelation coefficient: z z ( n 1) Measue of linea elationship. Magnitude Stength Sign Diection Bounded by +1.0 and Independent of scales of measuement. Conside intepetation of magnitude when elationship is not close to pefectly linea. Thee exists a tendency in pactice to ove-estimate stength of elationship implied by intemediate values of. May be elated to significance testing (late). Applet: Be consevative in intepeting stength of association. Conside othe infomation (late), and obtain and inspect scatteplots.

2 2 Types of coelation coefficients Peason: Usually conceived of as applicable to situations whee and ae inteval o atio scales (quantitative vaiables). But actually moe geneal: Applicable to othe kinds of vaiables. Conside dichotomous (binay) vaiables and anks. Phi coefficient: Suppose and ae both binay; e.g., test items. Data in fom of 2 2 fequency table: A B 1 C D Peason coelation fo binay and can be deived as: z z ( n 1) BC AD ( A + B)( C + D)( A + C)( B + D)

3 3 Called phi coefficient, designated φ. A special case of Peason coelation. Eithe fomula gives same esult. No need fo special softwae. Relationship between φ and χ 2 fo 2 2 table: φ 2 χ n Measues of association between two binay vaiables. Point-biseial coelation is binay, is quantitative (e.g., is a test item, is total test scoe). Let have values 0 and 1. p is popotion of sample scoing 1. q is popotion of sample scoing 0. sd p q 1 is mean of fo individuals scoing 1 on. 0 is mean of fo individuals scoing 0 on. Peason coelation between and can be deived as:

4 4 z z ( n 1) ( 1 0 ) sd p q Called point-biseial coelation; designated pb. Special case of Peason coelation; eithe fomula gives same esult; no need fo special softwae. Now conside two othe types of coelation coefficients involving binay vaiables, but not special cases of Peason coelation. Tetachoic coelation and ae binay (e.g., two test items). Define p, q, p, q. Phi coefficient gives obseved coelation. Tetachoic is an estimate of an unobseved coelation based on following concepts: Fo, assume thee exists a continuous undelying vaiable that follows a nomal distibution. A latent vaiable, call it L. is a binay measue of L.

5 5 A cutoff o theshold point on L divides the aea unde the cuve into two pats, p and q Latent Same assumption fo, defining L Latent Question: What is coelation between L and L?

6 This coelation is unobsevable, but can be estimated. Estimate is called tetachoic coelation. No simple fomula exists; no closed-fom algebaic expession. Special softwae equied fo computation. Not a special case of Peason coelation. Tetachoic is an estimated o infeed coelation. Fo same data, tetachoic > phi, based on assumption of impoved measuement of L. Can extend this appoach to case whee and each have multiple odeed categoies; e.g., Liket scales. Assume undelying continuous nomally-distibuted vaiables L and L. Nomal distibutions have multiple theshold points that epesent cutoffs fo categoies on and scales. Can estimate coelation between L and L as polychoic coelation. 6

7 7 Biseial coelation is binay, is quantitative; e.g., is a test item, is total test scoe. Obseved coelation between and is given by point-biseial. Biseial coelation is an estimate of an obseved coelation. Fo, assume thee exists a continuous undelying vaiable that follows a nomal distibution. A latent vaiable, call it L. is a binay measue of L. A cutoff o theshold point on L divides the aea unde the cuve into two pats, p and q Latent Question: What is coelation between L and?

8 8 This coelation is unobseved. Cannot be computed exactly, but can be estimated as biseial coelation. bis ( ) 0 1 ( h) sd p q whee h is odinate (height) of nomal cuve at value of z dividing aea into p and q. (Fom Table C). Relationship between biseial and point-biseial: bis pb p h q Fo same data, bis > pb. Biseial is not a special case of Peason coelation. It is an estimate of an unobsevable coelation. Requies special fomula.

9 9 Rank-Ode Coelation (Speaman) Given scoes on and, suppose we ae inteested only in ank ode of obsevations on these vaiables. Conside coelation between ank-odes. Convet and to anks, designated R and R. Obtain Peason coelation between anks. Simplified fomula: Let d be a new vaiable epesenting the diffeence in anks fo each peson: d R R Then the following expession fo Speaman s ankode coelation can be deived fom fomula fo Peason coelation: S 2 6 d 1 2 n( n 1) This is anothe special case of Peason coelation. Fomulas fo and S poduce same esult.

10 10 Summay: Have defined following coelation coefficients: Peason Phi Point-biseial Tetachoic Polychoic Biseial Rank-Ode Questions: What type of vaiables ae each of these designed fo? Which ones ae special cases of Peason coelation, and which ae not? Which ae obseved coelations, and which ae estimated o infeed coelations?

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.

In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. Radians At school we usually lean to measue an angle in degees. Howeve, thee ae othe ways of measuing an angle. One that we ae going to have a look at hee is measuing angles in units called adians. In

More information

Power and Sample Size Calculations for the 2-Sample Z-Statistic

Power and Sample Size Calculations for the 2-Sample Z-Statistic Powe and Sample Size Calculations fo the -Sample Z-Statistic James H. Steige ovembe 4, 004 Topics fo this Module. Reviewing Results fo the -Sample Z (a) Powe and Sample Size in Tems of a oncentality Paamete.

More information

Introduction to Electric Potential

Introduction to Electric Potential Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic

More information

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w 1.4 Rewite Fomulas and Equations Befoe You solved equations. Now You will ewite and evaluate fomulas and equations. Why? So you can apply geometic fomulas, as in Ex. 36. Key Vocabulay fomula solve fo a

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

Semipartial (Part) and Partial Correlation

Semipartial (Part) and Partial Correlation Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams

More information

LAL Update. Letter From the President. Dear LAL User:

LAL Update. Letter From the President. Dear LAL User: LAL Update ASSOCIATES OF CAPE COD, INCORPORATED OCTOBER 00 VOLUME 0, NO. Lette Fom the Pesident Dea LAL Use: This Update will claify some of the statistics used with tubidimetic and chomogenic LAL tests.

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

Problem Set # 9 Solutions

Problem Set # 9 Solutions Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new high-speed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease

More information

Solutions to Homework Set #5 Phys2414 Fall 2005

Solutions to Homework Set #5 Phys2414 Fall 2005 Solution Set #5 1 Solutions to Homewok Set #5 Phys414 Fall 005 Note: The numbes in the boxes coespond to those that ae geneated by WebAssign. The numbes on you individual assignment will vay. Any calculated

More information

LINES AND TANGENTS IN POLAR COORDINATES

LINES AND TANGENTS IN POLAR COORDINATES LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Pola-coodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

More information

International Monetary Economics Note 1

International Monetary Economics Note 1 36-632 Intenational Monetay Economics Note Let me biefly ecap on the dynamics of cuent accounts in small open economies. Conside the poblem of a epesentative consume in a county that is pefectly integated

More information

On Correlation Coefficient. The correlation coefficient indicates the degree of linear dependence of two random variables.

On Correlation Coefficient. The correlation coefficient indicates the degree of linear dependence of two random variables. C.Candan EE3/53-METU On Coelation Coefficient The coelation coefficient indicates the degee of linea dependence of two andom vaiables. It is defined as ( )( )} σ σ Popeties: 1. 1. (See appendi fo the poof

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

Gravitation. AP Physics C

Gravitation. AP Physics C Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What

More information

Questions for Review. By buying bonds This period you save s, next period you get s(1+r)

Questions for Review. By buying bonds This period you save s, next period you get s(1+r) MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume

More information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit

More information

CONCEPTUAL FRAMEWORK FOR DEVELOPING AND VERIFICATION OF ATTRIBUTION MODELS. ARITHMETIC ATTRIBUTION MODELS

CONCEPTUAL FRAMEWORK FOR DEVELOPING AND VERIFICATION OF ATTRIBUTION MODELS. ARITHMETIC ATTRIBUTION MODELS CONCEPUAL FAMEOK FO DEVELOPING AND VEIFICAION OF AIBUION MODELS. AIHMEIC AIBUION MODELS Yui K. Shestopaloff, is Diecto of eseach & Deelopment at SegmentSoft Inc. He is a Docto of Sciences and has a Ph.D.

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

Supplementary Material for EpiDiff

Supplementary Material for EpiDiff Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module

More information

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2  2 = GM . Combining the results we get ! Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation Newton, who extended the concept of inetia to all bodies, ealized that the moon is acceleating and is theefoe subject to a centipetal foce. He guessed that the foce that keeps the

More information

The Capital Asset Pricing Model. Chapter 9

The Capital Asset Pricing Model. Chapter 9 The Capital Asset Picing odel Chapte 9 Capital Asset Picing odel CAP centepiece of moden finance gives the elationship that should be obseved between isk and etun of an asset it allows fo the evaluation

More information

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players:

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players: CHAPT 11 TH GAVITATIONAL FILD (GAVITY) GAVITATIONAL FILD: The goundwok fo Newton s geat contibution to undestanding gavity was laid by thee majos playes: Newton s Law of Gavitation o gavitational and inetial

More information

Road tunnel. Road tunnel information sheet. Think about. Using the information

Road tunnel. Road tunnel information sheet. Think about. Using the information Road tunnel This activity is about using a gaphical o algebaic method to solve poblems in eal contets that can be modelled using quadatic epessions. The fist poblem is about a oad tunnel. The infomation

More information

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR John R. Gaham Adapted fom S. Viswanathan FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1 In this lectue we conside the effect of govenment

More information

CHAPTER 10 Aggregate Demand I

CHAPTER 10 Aggregate Demand I CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income

More information

1. How is the IS curve derived and what factors determine its slope? What happens to the slope of the IS curve if consumption is interest elastic?

1. How is the IS curve derived and what factors determine its slope? What happens to the slope of the IS curve if consumption is interest elastic? Chapte 7 Review Questions 1. How is the IS cuve deived and what factos detemine its slope? What happens to the slope of the IS cuve if consumption is inteest elastic? The IS cuve epesents equilibium in

More information

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon

More information

(3) Bipolar Transistor Current Sources

(3) Bipolar Transistor Current Sources B73 lectonics Analysis & Design (3) Bipola Tansisto Cuent Souces Leaning utcome Able to descibe and: Analyze and design a simple twotansisto BJT cuent-souce cicuit to poduce a given bias cuent. Analyze

More information

About the SAT Math Test

About the SAT Math Test Capte 18 About te SAT Mat Test Focus on Mat Tat Mattes Most A goup of select matematics skills and abilities contibutes te most to eadiness fo a college education and caee taining. Tese skills and abilities

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

Algebra and Trig. I. A point is a location or position that has no size or dimension.

Algebra and Trig. I. A point is a location or position that has no size or dimension. Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite

More information

1ST INTERNATIONAL CONFERENCE ON SUPPLY CHAINS

1ST INTERNATIONAL CONFERENCE ON SUPPLY CHAINS Examination of the inteelation among the ice of the fuel, the cost of tansot feight and the ofit magin Angeliki Paana 1, Aiadni Paana 2, Michael Dagiasis 3, Dimitios Folinas 4, Eaminontas Diamantooulos

More information

Skills Needed for Success in Calculus 1

Skills Needed for Success in Calculus 1 Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell

More information

Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key

Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key Instuctions Economics 1 Micoeconomic Theoy I Final Exam June 008 Faculty of Ats and Sciences ueen s Univesity Anse Key The exam is thee hous in length. The exam consists of to sections: Section A has five

More information

Mean-Reverting-Ebit-Based Stock Option Evaluation: Theory and Practice

Mean-Reverting-Ebit-Based Stock Option Evaluation: Theory and Practice Jounal of Applied Finance & aning, vol. 3, no. 5, 03, 35-36 ISSN: 79-6580 pint vesion, 79-6599 online Scienpess Ltd, 03 Mean-Reveting-bit-ased Stoc Option valuation: Theoy and Pactice Hassan l Ibami Abstact

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

Th Po er of th Cir l. Lesson3. Unit UNIT 6 GEOMETRIC FORM AND ITS FUNCTION

Th Po er of th Cir l. Lesson3. Unit UNIT 6 GEOMETRIC FORM AND ITS FUNCTION Lesson3 Th Po e of th Ci l Quadilateals and tiangles ae used to make eveyday things wok. Right tiangles ae the basis fo tigonometic atios elating angle measues to atios of lengths of sides. Anothe family

More information

Lesson 32: Measuring Circular Motion

Lesson 32: Measuring Circular Motion Lesson 32: Measuing Cicula Motion Velocity hee should be a way to come up with a basic fomula that elates velocity in icle to some of the basic popeties of icle. Let s ty stating off with a fomula that

More information

NUCLEAR MAGNETIC RESONANCE

NUCLEAR MAGNETIC RESONANCE 19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic

More information

Physics: Electromagnetism Spring PROBLEM SET 6 Solutions

Physics: Electromagnetism Spring PROBLEM SET 6 Solutions Physics: Electomagnetism Sping 7 Physics: Electomagnetism Sping 7 PROBEM SET 6 Solutions Electostatic Enegy Basics: Wolfson and Pasachoff h 6 Poblem 7 p 679 Thee ae si diffeent pais of equal chages and

More information

Chapter 3: Vectors and Coordinate Systems

Chapter 3: Vectors and Coordinate Systems Coodinate Systems Chapte 3: Vectos and Coodinate Systems Used to descibe the position of a point in space Coodinate system consists of a fied efeence point called the oigin specific aes with scales and

More information

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

More information

The Critical Angle and Percent Efficiency of Parabolic Solar Cookers

The Critical Angle and Percent Efficiency of Parabolic Solar Cookers The Citical Angle and Pecent Eiciency o Paabolic Sola Cookes Aiel Chen Abstact: The paabola is commonly used as the cuve o sola cookes because o its ability to elect incoming light with an incoming angle

More information

A study modeling of 15 days cumulative rainfall at Purajaya Region, Bandar Lampung, Indonesia

A study modeling of 15 days cumulative rainfall at Purajaya Region, Bandar Lampung, Indonesia A study modeling of 15 days cumulative ainfall at Puajaya Region, Banda Lampung, Indonesia Ahmad Zakaia* Abstact Aim of this eseach is to study peiodic modeling of 15 days cumulative ainfall time seies.

More information

1.1 KINEMATIC RELATIONSHIPS

1.1 KINEMATIC RELATIONSHIPS 1.1 KINEMATIC RELATIONSHIPS Thoughout the Advanced Highe Physics couse calculus techniques will be used. These techniques ae vey poweful and knowledge of integation and diffeentiation will allow a deepe

More information

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to . Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate

More information

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuent-caying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to

More information

VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY OF BIO-DIESEL FUELS VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use

More information

TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS 14. NEWTON'S RINGS

TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS 14. NEWTON'S RINGS 4. NEWTON'S RINGS. Obective Detemining adius of cuvatue of a long focal length plano-convex lens (lage adius of cuvatue).. Equipment needed Measuing micoscope, plano-convex long focal length lens, monochomatic

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses, 3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects

More information

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles TRIGONOMETRY REVIEW The Cosines and Sines of the Standad Angles P θ = ( cos θ, sin θ ) . ANGLES AND THEIR MEASURE In ode to define the tigonometic functions so that they can be used not only fo tiangula

More information

Mechanics 1: Motion in a Central Force Field

Mechanics 1: Motion in a Central Force Field Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.

More information

The Binomial Distribution

The Binomial Distribution The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between

More information

Chapter 6. Gradually-Varied Flow in Open Channels

Chapter 6. Gradually-Varied Flow in Open Channels Chapte 6 Gadually-Vaied Flow in Open Channels 6.. Intoduction A stea non-unifom flow in a pismatic channel with gadual changes in its watesuface elevation is named as gadually-vaied flow (GVF). The backwate

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

CS 229 Project : Improving on Yelp Reviews Using NLP and Bayesian Scoring

CS 229 Project : Improving on Yelp Reviews Using NLP and Bayesian Scoring CS 9 Poject : Impoving on Yelp Reviews Using NLP and Bayesian Scoing Patick Bechon pbechon@stanfod.edu Léo Gimaldi leo.gimaldi@stanfod.edu Yacine Meouchi meouchi@stanfod.edu. INTRODUCTION Yelp allows its

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

Open Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy

Open Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy Chapte 32. A Macoeconomic Theoy of the Open Economy Open Economies An open economy is one that inteacts feely with othe economies aound the wold. slide 0 slide 1 Key Macoeconomic Vaiables in an Open Economy

More information

Do Vibrations Make Sound?

Do Vibrations Make Sound? Do Vibations Make Sound? Gade 1: Sound Pobe Aligned with National Standads oveview Students will lean about sound and vibations. This activity will allow students to see and hea how vibations do in fact

More information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate Systems L. M. Kalnins, March 2009 Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean

More information

Physics 505 Homework No. 5 Solutions S5-1. 1. Angular momentum uncertainty relations. A system is in the lm eigenstate of L 2, L z.

Physics 505 Homework No. 5 Solutions S5-1. 1. Angular momentum uncertainty relations. A system is in the lm eigenstate of L 2, L z. Physics 55 Homewok No. 5 s S5-. Angula momentum uncetainty elations. A system is in the lm eigenstate of L 2, L z. a Show that the expectation values of L ± = L x ± il y, L x, and L y all vanish. ψ lm

More information

The Grating Spectrometer and Atomic Spectra

The Grating Spectrometer and Atomic Spectra PHY 19 Gating Spectomete 1 The Gating Spectomete and Atomic Specta Intoduction In the pevious expeiment diffaction and intefeence wee discussed and at the end a diffaction gating was intoduced. In this

More information

12.1. FÖRSTER RESONANCE ENERGY TRANSFER

12.1. FÖRSTER RESONANCE ENERGY TRANSFER ndei Tokmakoff, MIT epatment of Chemisty, 3/5/8 1-1 1.1. FÖRSTER RESONNCE ENERGY TRNSFER Föste esonance enegy tansfe (FR) efes to the nonadiative tansfe of an electonic excitation fom a dono molecule to

More information

2008 Quarter-Final Exam Solutions

2008 Quarter-Final Exam Solutions 2008 Quate-final Exam - Solutions 1 2008 Quate-Final Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of

More information

Theory and practise of the g-index

Theory and practise of the g-index Theoy and pactise of the g-index by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B-3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,

More information

Trigonometric Functions of Any Angle

Trigonometric Functions of Any Angle Tigonomet Module T2 Tigonometic Functions of An Angle Copight This publication The Nothen Albeta Institute of Technolog 2002. All Rights Reseved. LAST REVISED Decembe, 2008 Tigonometic Functions of An

More information

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation

More information

PY1052 Problem Set 3 Autumn 2004 Solutions

PY1052 Problem Set 3 Autumn 2004 Solutions PY1052 Poblem Set 3 Autumn 2004 Solutions C F = 8 N F = 25 N 1 2 A A (1) A foce F 1 = 8 N is exeted hoizontally on block A, which has a mass of 4.5 kg. The coefficient of static fiction between A and the

More information

Database Management Systems

Database Management Systems Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012

More information

DYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES

DYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation

More information

Financing Terms in the EOQ Model

Financing Terms in the EOQ Model Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad

More information

&RQYHUWLQJ:DYH$XGLR)LOHV %URRNWURXW $SSOLFDWLRQ1RWH

&RQYHUWLQJ:DYH$XGLR)LOHV %URRNWURXW $SSOLFDWLRQ1RWH &RQYHUWLQJ:DYH$XGLR)LOHV %URRNWURXW $SSOLFDWLRQ1RWH Conveting Wave Audio Files, Pat Numbe 00-00-3504, Revision 1.10, June 1999 Copyight by Booktout Technology, Inc. This manual is copyighted and all ights

More information

An Epidemic Model of Mobile Phone Virus

An Epidemic Model of Mobile Phone Virus An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity

More information

Fluids Lecture 15 Notes

Fluids Lecture 15 Notes Fluids Lectue 15 Notes 1. Unifom flow, Souces, Sinks, Doublets Reading: Andeson 3.9 3.12 Unifom Flow Definition A unifom flow consists of a velocit field whee V = uî + vĵ is a constant. In 2-D, this velocit

More information

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 Problem Set 8 Autumn 2004 Solutions PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what

More information

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

Heat transfer has direction as well as magnitude. The rate of heat conduction

Heat transfer has direction as well as magnitude. The rate of heat conduction HEAT CONDUCTION EQUATION CHAPTER 2 Heat tansfe has diection as well as magnitude. The ate of heat conduction in a specified diection is popotional to the tempeatue gadient, which is the ate of change in

More information

UNIVERSIDAD DE CANTABRIA TESIS DOCTORAL

UNIVERSIDAD DE CANTABRIA TESIS DOCTORAL UNIVERSIDAD DE CANABRIA Depatamento de Ingenieía de Comunicaciones ESIS DOCORAL Cyogenic echnology in the Micowave Engineeing: Application to MIC and MMIC Vey Low Noise Amplifie Design Juan Luis Cano de

More information

P S. Estimation of the simple correlation coefficient GWOWEN SHIEH

P S. Estimation of the simple correlation coefficient GWOWEN SHIEH Behavio Reseach Methods 00, 4 (4), 906-97 doi:0.3758/brm.4.4.906 Estimation of the simple coelation coefficient GWOWE SHIEH ational Chiao Tung Univesity, Hsinchu, Taiwan This aticle investigates some unfamilia

More information

Exam I. Spring 2004 Serway & Jewett, Chapters 1-5. Fill in the bubble for the correct answer on the answer sheet. next to the number.

Exam I. Spring 2004 Serway & Jewett, Chapters 1-5. Fill in the bubble for the correct answer on the answer sheet. next to the number. Agin/Meye PART I: QUALITATIVE Exam I Sping 2004 Seway & Jewett, Chaptes 1-5 Assigned Seat Numbe Fill in the bubble fo the coect answe on the answe sheet. next to the numbe. NO PARTIAL CREDIT: SUBMIT ONE

More information

Alignment of Buckingham Parameters to Generalized Lennard-Jones Potential Functions

Alignment of Buckingham Parameters to Generalized Lennard-Jones Potential Functions Alignment of Buckingham Paametes to Genealized Lennad-Jones Potential Functions Teik-Cheng Lim School of Science and Technology SIM Univesity 535A Clementi oad S 599490 epublic of Singapoe epint equests

More information

UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

More information

Chapter 23: Gauss s Law

Chapter 23: Gauss s Law Chapte 3: Gauss s Law Homewok: Read Chapte 3 Questions, 5, 1 Poblems 1, 5, 3 Gauss s Law Gauss s Law is the fist of the fou Maxwell Equations which summaize all of electomagnetic theoy. Gauss s Law gives

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Hamonic Motion Intoduction Simple hamonic motion occus when the net foce acting on an object is popotional to the object s displacement fom an equilibium position. When the object is at an equilibium

More information

Lab 5: Circular Motion

Lab 5: Circular Motion Lab 5: Cicula motion Physics 193 Fall 2006 Lab 5: Cicula Motion I. Intoduction The lab today involves the analysis of objects that ae moving in a cicle. Newton s second law as applied to cicula motion

More information

Macroeconomics I. Antonio Zabalza. University of Valencia 1. Class 5. The IS-LM model and Aggregate Demand

Macroeconomics I. Antonio Zabalza. University of Valencia 1. Class 5. The IS-LM model and Aggregate Demand Macoeconomics I. Antonio Zabalza. Univesity of Valencia 1 Class 5. The IS-LM model and Aggegate Demand 1. Use the Keynesian coss to pedict the impact of: a) An incease in govenment puchases. b) An incease

More information

Chapter F. Magnetism. Blinn College - Physics Terry Honan

Chapter F. Magnetism. Blinn College - Physics Terry Honan Chapte F Magnetism Blinn College - Physics 46 - Tey Honan F. - Magnetic Dipoles and Magnetic Fields Electomagnetic Duality Thee ae two types of "magnetic chage" o poles, Noth poles N and South poles S.

More information

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field

More information

Cubic Spline Interpolation by Solving a Recurrence Equation Instead of a Tridiagonal Matrix

Cubic Spline Interpolation by Solving a Recurrence Equation Instead of a Tridiagonal Matrix Matematical Metods in Science and Engineeing Cubic Spline Intepolation by Solving a Recuence Equation Instead of a Tidiagonal Matix Pete Z Revesz Depatment of Compute Science and Engineeing Univesity of

More information

Modern Linear Algebra

Modern Linear Algebra Hochschule fü Witschaft und Recht Belin Belin School of Economics and Law Wintesemeste 04/05 D. Hon Mathematics fo Business and Economics LV-N. 0069.0 Moden Linea Algeba (A Geometic Algeba cash couse,

More information