[ L] υ = (3) [ L] n. Q: What are the units of K in Eq. (3)? (Why is units placed in quotations.) What is the relationship to K in Eq. (1)?
|
|
|
- Ruby Higgins
- 5 years ago
- Views:
Transcription
1 Chem 78 Spr. M. Wes Bdg Polyomals Bdg Polyomals We ve looked at three cases of lgad bdg so far: The sgle set of depedet stes (ss[]s [ ] [ ] Multple sets of depedet stes (ms[]s, or m[]ss All or oe, or two-state cooperatvty ( [ ] [ ] ( m [ ] [ ] ( ( & ( are the lmtg cases of o cooperatve teractos, ad very strog cooperatve teractos, respectvely, for a system wth oe type of bdg ste. Q: What are the uts of Eq. (? (Why s uts placed quotatos. What s the relatoshp to Eq. (? Equatos to spell out the statstcal dstrbutos of prote mcrostates, wth specfc referece to the extet of lgad bdg (ad assumptos about the ature of the bdg. I geeral, the umerator of υ accouts for the umber of moles of boud lgad, ad the deomator accouts for the umber moles of prote. The geeral case wth bdg stes s wrtte as [ P] [ P ] [ P ] [ P ] [ P] [ P] [ P ] [ P ] [ P ] ( Have there bee assumptos made about whether the stes teract, or whether there s oe or more class of stes? (The aswer to both s o, hece ts geeralty. Also, wthout loss of geeralty, substtutos ca be made for the P (where rages from 0 to. [ P][ ] [ P][ ] [ P][ ] [ P][ ] [ P] [ P][ ] [ P][ ] [ P][ ] [ P][ ] (5 page
2 Chem 78 Spr. M. Wes Bdg Polyomals From here, relatoshps amog bdg costats ca be assumed ad the exploted Equato 5 to reach Equatos to. Some of the subtletes Equato 5 are, part, a matter of defto. through are macroscopc assocato costats; the relatoshp to the uderlyg trsc costat(s wll chage accordg to the umber of sets (or classes of stes, ad the ature of the teracto amog stes,.e. are there teractos, or ot. I all cases [P] ca be factored out to gve: [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] ( Factorg out [P] mplctly ackowledges t ([P] as a referece state wth respect to statstcal ad eergetc cosderatos, more o ths below. Q: What are the expressos for terms of the trsc assocato costats, f ( there s a sgle set of depedet stes, ( there are sets of depedet stes, ( there s oe set of strogly (all or oe teractg stes? SSS. The relatoshp betwee the macroscopc assocato costats ad a sgle trsc assocato costat (, smply reflects the statstcs of lgad bdg through a sgle class of stes. The dvdual steps of the bdg process, catalogued accordg to the umber of lgads boud, are gve by P P [P]/[P][] P P [P ]/[P][] P P [P ]/[P ][] (7 P - P [P ]/[P - ][] The (macroscopc costats are related to (the trsc costat by Ω, (8 Ω, where Ω, ad Ω,- represet the umber of ways of assortg ad - lgad molecules, respectvely, o depedet, equvalet bdg stes.! Ω (9, (!! Equato 9 s recogzable as the equato for coeffcets of the bomal expaso. For small values of, e.g., the valdty of the Equatos 8 ad 9 geeratg the page
3 Chem 78 Spr Bdg Polyomals. M. Wes page relatoshps betwee the ad ca be valdated by eumeratg the dfferet mcroscopc forms of P ad P - dagrammatcally. Cosder the stuato wth stes. I Equato 0, the formulae for the, expressed terms of (va Equato 8 have bee substtuted to Equato 5 ( [ ] ( ( [ ] ( ( ( [ ] ( ( ( ( [ ] ( [ ] ( ( [ ] ( ( ( [ ] ( ( ( ( [ ] υ (0 The terms the umerator are collected such as fasho to accetuate the umber of stes (. ( [ ] ( [ ] ( [ ] ( [ ] [ ] [ ] [ ] [ ] υ ( Factorg out [] the umerator produces a rd order polyomal. The deomator s a th order polyomal. [ ] [ ] [ ] [ ] { } [ ] [ ] [ ] [ ] υ ( Both of these are of the form ( [], [ ] [ ] ( [ ] ( [ ] [ ] ( υ ( Geeralzg to stes gves Equato. The Partto Fucto, Q. The deomator of Equato s equal to the total prote cocetrato dvded by the cocetrato of free prote s [P] tot /[P]. Ths quatty has meag statstcal mechacs; t s a example of a partto fucto, Q. [ ] [ ] [ ] [ ] Q ( Q s the sum of the umber of ways a gve eergy state may be formed. [P], represeted by the leadg term o the rght had sde of Equato, s the referece state ad has a relatve eergy equal to, ad a statstcal factor equal to. The partto fucto for the equvalet stes (sss model wth stes s [ ] [ ] [ ] [ ] Q (5 Whe wrtte a slghtly dfferet way, as Equato,
4 Chem 78 Spr. M. Wes Bdg Polyomals [ ] 0 [ ] [ ] [ ] [ ] Q 0 ( shows explctly the cotrbutos from statstcs (the lead umercal coeffcets ad terms that represet the eerges of the dfferet prote forms wth oe or more lgad molecules boud ( []. These are relatve eergy terms, relatve to the eergy of the referece state [P], ad are also kow as statstcal weghts (they weght the statstcal cotrbuto. Q, for the geeral case for equvalet bdg stes s Q 0 Ω [ ], (7 Each term the summato of Equato 7 s the product betwee the umber of dstgushable mcroscopc arragemets (Ω, ad the statstcal weght, []. ([] s sometmes referred to as the reduced lgad cocetrato. The [] represet ratos of prote forms, e.g. [P ]/[P], a Boltzma-lke maer, [P ]/[P] exp[δg/k B T], where Δg Δg 0 k B Tl[]. The progressve bdg of lgad cremetally adds to the statstcal weght. Note that for the depedet stes model, the eergy cremet s the same for each lgad molecule that bds to the prote: statstcal weght ato Δg 0 0 [] 0 [P]/[P] 0 [] [P]/[P] Δg [] [P ]/[P] Δg [] [P ]/[P] Δg [] [P ]/[P] Δg Fally, t s terestg to ote that ( [ ] dq dlq (8 Q d ( [ ] dl( [ ] Dscussos of the relatoshp betwee expermetal observables ad the partto fucto, of whch Equato 8 s a example, are foud statstcal thermodyamcs ad bophyscs textbooks. Two Models of Fte Cooperatvty Cooperatvty s rarely adequately descrbed by a all or oe scearo, so other models have bee developed. Two wdely used models are the cocerted ad sequetal models. page
5 Chem 78 Spr. M. Wes Bdg Polyomals. The Mood-Wyma-Chageux (MWC, or cocerted, model was publshed 95. A cetral assumpto s that cooperatve protes cosst of a olgomerc cluster of protomers (subuts, whch all the protomers are the same coformato, although the prote ca udergo a trasto betwee (at least two coformatoal states a cocerted fasho. The dfferet coformatos have dfferet lgad bdg afftes. The detals of the assumptos are foud the paper that descrbed the model: Mood, Wyma & Chageux. 95. J. Mol. Bol., (Posted o the course webste. Also, see Cator & Schmmel, Vol. III, Chapter 7 the full referece for ths book s o the course webste. The two assumptos of the MWC model ( that two coformatos of the macromolecule are assumed, ad ( that a dfferece bdg affty exsts betwee these two forms, are combed a way that geerates postve cooperatvty. The relaxed ( ad tese (T forms of the macromolecule, each egage lgad bdg equlbra. (Here the lgad s represeted by the letter F. F F T F TF F F F TF F TF F F F TF F TF (9 F - F F TF - F TF A equlbrum, whch exsts betwee the ad T forms the absece of lgad, s gve by T 0 [T]/[] (0 where 0 s geerally greater tha oe, whch s mples that the T form (the low affty form s more stable tha the form the absece of lgad. The relatoshp betwee lgad bdg costats to the T ad forms, whch are characterzed by the trsc assocato costats T ad, respectvely, s gve by c T / ( By defto the T form bds lgad less tghtly tha the form, c <. The average degree of saturato takes o a specfc form, whch s llustrated by a prote wth four lgad-bdg stes [ F] [ F ] [ F ] [ F ] [ TF] [ TF ] [ TF ] [ TF ] [ ] [ F] [ F ] [ F ] [ F ] [ T] [ TF] [ TF ] [ TF ] [ TF ] ( Factorg the polyomals the same maer, as had bee doe for the sgle stes model, gves page 5
6 Chem 78 Spr. M. Wes Bdg Polyomals [ ][ F] ( [ F] T[ T][ F] ( T[ F] [ ] ( [ F] [ T] ( [ F] ( Applcato of the deftos for c ( T c ad 0 ([T] 0 [] allows [T] ad T to be factored out [ F] ( [ F] c0[ F] ( c[ F] ( [ F] ( c [ F] ( Geeralzato to the prote that has bdg stes, gves [ F] ( [ F] c0[ F] ( c[ F] ( [ F] ( c [ F] 0 (5 0 T What values of c ad 0 must take o to reduce to ether ( the sgle-set-of-stes model, or ( the all-or-oe model?. The oshlad-nemethy-flmer (NF Sequetal Model geerates cooperatvty by allowg the trsc costats chage a way that reflects the chagg probablty of a prote subut to udergo the lgad-depedet trasto from a low to a hgh affty state, whch s flueced by lgad bdg to oe (or more eghborg subuts. A two-ste model suffces to llustrate the pot [ F] [ F] [ F] [ F] ( where ad are trsc bdg costats. I the sequetal model, < dcates postve cooperatvty, > dcates egatve cooperatvty, ad dcates depedet stes. The exact ature of the bdg polyomal ad the teracto terms depeds o the symmetry of the macromolecule. See the orgal referece for detals. (oshlad, Nemethy ad Flmer. 9. Bochemstry. 5:5-85; posted at the course webste page
Multiple Choice Test. Chapter Adequacy of Models for Regression
Multple Choce Test Chapter 06.0 Adequac of Models for Regresso. For a lear regresso model to be cosdered adequate, the percetage of scaled resduals that eed to be the rage [-,] s greater tha or equal to
The Mathematical Appendix
The Mathematcal Appedx Defto A: If ( Λ, Ω, where ( λ λ λ whch the probablty dstrbutos,,..., Defto A. uppose that ( Λ,,..., s a expermet type, the σ-algebra o λ λ λ are defed s deoted by ( (,,...,, σ Ω.
Applying the condition for equilibrium to this equilibrium, we get (1) n i i =, r G and 5 i
CHEMICAL EQUILIBRIA The Thermodyamc Equlbrum Costat Cosder a reversble reacto of the type 1 A 1 + 2 A 2 + W m A m + m+1 A m+1 + Assgg postve values to the stochometrc coeffcets o the rght had sde ad egatve
d dt d d dt dt Also recall that by Taylor series, / 2 (enables use of sin instead of cos-see p.27 of A&F) dsin
Learzato of the Swg Equato We wll cover sectos.5.-.6 ad begg of Secto 3.3 these otes. 1. Sgle mache-fte bus case Cosder a sgle mache coected to a fte bus, as show Fg. 1 below. E y1 V=1./_ Fg. 1 The admttace
Lecture 07: Poles and Zeros
Lecture 07: Poles ad Zeros Defto of poles ad zeros The trasfer fucto provdes a bass for determg mportat system respose characterstcs wthout solvg the complete dfferetal equato. As defed, the trasfer fucto
Chapter 5 Properties of a Random Sample
Lecture 6 o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for the prevous lecture Cocepts: t-dstrbuto, F-dstrbuto Theorems: Dstrbutos of sample mea ad sample varace, relatoshp betwee sample mea ad sample
Parameter, Statistic and Random Samples
Parameter, Statstc ad Radom Samples A parameter s a umber that descrbes the populato. It s a fxed umber, but practce we do ot kow ts value. A statstc s a fucto of the sample data,.e., t s a quatty whose
Chapter Statistics Background of Regression Analysis
Chapter 06.0 Statstcs Backgroud of Regresso Aalyss After readg ths chapter, you should be able to:. revew the statstcs backgroud eeded for learg regresso, ad. kow a bref hstory of regresso. Revew of Statstcal
Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model
Lecture 7. Cofdece Itervals ad Hypothess Tests the Smple CLR Model I lecture 6 we troduced the Classcal Lear Regresso (CLR) model that s the radom expermet of whch the data Y,,, K, are the outcomes. The
Summary of the lecture in Biostatistics
Summary of the lecture Bostatstcs Probablty Desty Fucto For a cotuos radom varable, a probablty desty fucto s a fucto such that: 0 dx a b) b a dx A probablty desty fucto provdes a smple descrpto of the
CHAPTER VI Statistical Analysis of Experimental Data
Chapter VI Statstcal Aalyss of Expermetal Data CHAPTER VI Statstcal Aalyss of Expermetal Data Measuremets do ot lead to a uque value. Ths s a result of the multtude of errors (maly radom errors) that ca
Third handout: On the Gini Index
Thrd hadout: O the dex Corrado, a tala statstca, proposed (, 9, 96) to measure absolute equalt va the mea dfferece whch s defed as ( / ) where refers to the total umber of dvduals socet. Assume that. The
Analysis of Variance with Weibull Data
Aalyss of Varace wth Webull Data Lahaa Watthaacheewaul Abstract I statstcal data aalyss by aalyss of varace, the usual basc assumptos are that the model s addtve ad the errors are radomly, depedetly, ad
best estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best
Error Aalyss Preamble Wheever a measuremet s made, the result followg from that measuremet s always subject to ucertaty The ucertaty ca be reduced by makg several measuremets of the same quatty or by mprovg
Chapter 8. Inferences about More Than Two Population Central Values
Chapter 8. Ifereces about More Tha Two Populato Cetral Values Case tudy: Effect of Tmg of the Treatmet of Port-We tas wth Lasers ) To vestgate whether treatmet at a youg age would yeld better results tha
Econometric Methods. Review of Estimation
Ecoometrc Methods Revew of Estmato Estmatg the populato mea Radom samplg Pot ad terval estmators Lear estmators Ubased estmators Lear Ubased Estmators (LUEs) Effcecy (mmum varace) ad Best Lear Ubased Estmators
Chapter 4 Multiple Random Variables
Revew for the prevous lecture: Theorems ad Examples: How to obta the pmf (pdf) of U = g (, Y) ad V = g (, Y) Chapter 4 Multple Radom Varables Chapter 44 Herarchcal Models ad Mxture Dstrbutos Examples:
Evaluating Polynomials
Uverst of Nebraska - Lcol DgtalCommos@Uverst of Nebraska - Lcol MAT Exam Expostor Papers Math the Mddle Isttute Partershp 7-7 Evaluatg Polomals Thomas J. Harrgto Uverst of Nebraska-Lcol Follow ths ad addtoal
Lecture 3 Probability review (cont d)
STATS 00: Itroducto to Statstcal Iferece Autum 06 Lecture 3 Probablty revew (cot d) 3. Jot dstrbutos If radom varables X,..., X k are depedet, the ther dstrbuto may be specfed by specfyg the dvdual dstrbuto
CHAPTER 4 RADICAL EXPRESSIONS
6 CHAPTER RADICAL EXPRESSIONS. The th Root of a Real Number A real umber a s called the th root of a real umber b f Thus, for example: s a square root of sce. s also a square root of sce ( ). s a cube
We have already referred to a certain reaction, which takes place at high temperature after rich combustion.
ME 41 Day 13 Topcs Chemcal Equlbrum - Theory Chemcal Equlbrum Example #1 Equlbrum Costats Chemcal Equlbrum Example #2 Chemcal Equlbrum of Hot Bured Gas 1. Chemcal Equlbrum We have already referred to a
Introduction to local (nonparametric) density estimation. methods
Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest
A Primer on Summation Notation George H Olson, Ph. D. Doctoral Program in Educational Leadership Appalachian State University Spring 2010
Summato Operator A Prmer o Summato otato George H Olso Ph D Doctoral Program Educatoal Leadershp Appalacha State Uversty Sprg 00 The summato operator ( ) {Greek letter captal sgma} s a structo to sum over
ENGI 3423 Simple Linear Regression Page 12-01
ENGI 343 mple Lear Regresso Page - mple Lear Regresso ometmes a expermet s set up where the expermeter has cotrol over the values of oe or more varables X ad measures the resultg values of aother varable
Mu Sequences/Series Solutions National Convention 2014
Mu Sequeces/Seres Solutos Natoal Coveto 04 C 6 E A 6C A 6 B B 7 A D 7 D C 7 A B 8 A B 8 A C 8 E 4 B 9 B 4 E 9 B 4 C 9 E C 0 A A 0 D B 0 C C Usg basc propertes of arthmetc sequeces, we fd a ad bm m We eed
Estimation of Stress- Strength Reliability model using finite mixture of exponential distributions
Iteratoal Joural of Computatoal Egeerg Research Vol, 0 Issue, Estmato of Stress- Stregth Relablty model usg fte mxture of expoetal dstrbutos K.Sadhya, T.S.Umamaheswar Departmet of Mathematcs, Lal Bhadur
Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses
Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s
Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses
Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s
Functions of Random Variables
Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,
hp calculators HP 30S Statistics Averages and Standard Deviations Average and Standard Deviation Practice Finding Averages and Standard Deviations
HP 30S Statstcs Averages ad Stadard Devatos Average ad Stadard Devato Practce Fdg Averages ad Stadard Devatos HP 30S Statstcs Averages ad Stadard Devatos Average ad stadard devato The HP 30S provdes several
X ε ) = 0, or equivalently, lim
Revew for the prevous lecture Cocepts: order statstcs Theorems: Dstrbutos of order statstcs Examples: How to get the dstrbuto of order statstcs Chapter 5 Propertes of a Radom Sample Secto 55 Covergece
ρ < 1 be five real numbers. The
Lecture o BST 63: Statstcal Theory I Ku Zhag, /0/006 Revew for the prevous lecture Deftos: covarace, correlato Examples: How to calculate covarace ad correlato Theorems: propertes of correlato ad covarace
Long Tailed functions
Log Taled fuctos Log tal fuctos are desrable for fttg may physologcal data sets A geeral example s fttg the respose of a system to a mpulse put Most passve systems have u modal rght skewed respose fuctos
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Postpoed exam: ECON430 Statstcs Date of exam: Jauary 0, 0 Tme for exam: 09:00 a.m. :00 oo The problem set covers 5 pages Resources allowed: All wrtte ad prted
Tandem-repeat Promoter Strength Prediction Model.(Abbreviation: TP Model)
Tadem-repeat Promoter Predcto Model.(Abbrevato: TP Model) Cotet: 1.Overvew 2.Symbol table, assumptos ad reasos 3.Modelg result 4.Model dervato 5.Dscusso 6.User gudele 1. Overvew Ths model ams at predctg
THE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA
THE ROYAL STATISTICAL SOCIETY 3 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA PAPER I STATISTICAL THEORY & METHODS The Socety provdes these solutos to assst caddates preparg for the examatos future years ad
Objectives of Multiple Regression
Obectves of Multple Regresso Establsh the lear equato that best predcts values of a depedet varable Y usg more tha oe eplaator varable from a large set of potetal predctors {,,... k }. Fd that subset of
Lecture 3. Sampling, sampling distributions, and parameter estimation
Lecture 3 Samplg, samplg dstrbutos, ad parameter estmato Samplg Defto Populato s defed as the collecto of all the possble observatos of terest. The collecto of observatos we take from the populato s called
Chapter 14 Logistic Regression Models
Chapter 4 Logstc Regresso Models I the lear regresso model X β + ε, there are two types of varables explaatory varables X, X,, X k ad study varable y These varables ca be measured o a cotuous scale as
MA 524 Homework 6 Solutions
MA 524 Homework 6 Solutos. Sce S(, s the umber of ways to partto [] to k oempty blocks, ad c(, s the umber of ways to partto to k oempty blocks ad also the arrage each block to a cycle, we must have S(,
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Exam: ECON430 Statstcs Date of exam: Frday, December 8, 07 Grades are gve: Jauary 4, 08 Tme for exam: 0900 am 00 oo The problem set covers 5 pages Resources allowed:
8.1 Hashing Algorithms
CS787: Advaced Algorthms Scrbe: Mayak Maheshwar, Chrs Hrchs Lecturer: Shuch Chawla Topc: Hashg ad NP-Completeess Date: September 21 2007 Prevously we looked at applcatos of radomzed algorthms, ad bega
22 Nonparametric Methods.
22 oparametrc Methods. I parametrc models oe assumes apror that the dstrbutos have a specfc form wth oe or more ukow parameters ad oe tres to fd the best or atleast reasoably effcet procedures that aswer
Extreme Value Theory: An Introduction
(correcto d Extreme Value Theory: A Itroducto by Laures de Haa ad Aa Ferrera Wth ths webpage the authors ted to form the readers of errors or mstakes foud the book after publcato. We also gve extesos for
The E vs k diagrams are in general a function of the k -space direction in a crystal
vs dagram p m m he parameter s called the crystal mometum ad s a parameter that results from applyg Schrödger wave equato to a sgle-crystal lattce. lectros travelg dfferet drectos ecouter dfferet potetal
Multiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades
STAT 101 Dr. Kar Lock Morga 11/20/12 Exam 2 Grades Multple Regresso SECTIONS 9.2, 10.1, 10.2 Multple explaatory varables (10.1) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (10.2) Trasformatos
Chapter 4 Multiple Random Variables
Revew o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for Chapter 4-5 Notes: Although all deftos ad theorems troduced our lectures ad ths ote are mportat ad you should be famlar wth, but I put those
Ordinary Least Squares Regression. Simple Regression. Algebra and Assumptions.
Ordary Least Squares egresso. Smple egresso. Algebra ad Assumptos. I ths part of the course we are gog to study a techque for aalysg the lear relatoshp betwee two varables Y ad X. We have pars of observatos
LECTURE - 4 SIMPLE RANDOM SAMPLING DR. SHALABH DEPARTMENT OF MATHEMATICS AND STATISTICS INDIAN INSTITUTE OF TECHNOLOGY KANPUR
amplg Theory MODULE II LECTURE - 4 IMPLE RADOM AMPLIG DR. HALABH DEPARTMET OF MATHEMATIC AD TATITIC IDIA ITITUTE OF TECHOLOGY KAPUR Estmato of populato mea ad populato varace Oe of the ma objectves after
General Method for Calculating Chemical Equilibrium Composition
AE 6766/Setzma Sprg 004 Geeral Metod for Calculatg Cemcal Equlbrum Composto For gve tal codtos (e.g., for gve reactats, coose te speces to be cluded te products. As a example, for combusto of ydroge wt
MEASURES OF DISPERSION
MEASURES OF DISPERSION Measure of Cetral Tedecy: Measures of Cetral Tedecy ad Dsperso ) Mathematcal Average: a) Arthmetc mea (A.M.) b) Geometrc mea (G.M.) c) Harmoc mea (H.M.) ) Averages of Posto: a) Meda
Descriptive Statistics
Page Techcal Math II Descrptve Statstcs Descrptve Statstcs Descrptve statstcs s the body of methods used to represet ad summarze sets of data. A descrpto of how a set of measuremets (for eample, people
Chapter 11 The Analysis of Variance
Chapter The Aalyss of Varace. Oe Factor Aalyss of Varace. Radomzed Bloc Desgs (ot for ths course) NIPRL . Oe Factor Aalyss of Varace.. Oe Factor Layouts (/4) Suppose that a expermeter s terested populatos
Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn:
Chapter 3 3- Busess Statstcs: A Frst Course Ffth Edto Chapter 2 Correlato ad Smple Lear Regresso Busess Statstcs: A Frst Course, 5e 29 Pretce-Hall, Ic. Chap 2- Learg Objectves I ths chapter, you lear:
Statistics Descriptive and Inferential Statistics. Instructor: Daisuke Nagakura
Statstcs Descrptve ad Iferetal Statstcs Istructor: Dasuke Nagakura (agakura@z7.keo.jp) 1 Today s topc Today, I talk about two categores of statstcal aalyses, descrptve statstcs ad feretal statstcs, ad
Statistics: Unlocking the Power of Data Lock 5
STAT 0 Dr. Kar Lock Morga Exam 2 Grades: I- Class Multple Regresso SECTIONS 9.2, 0., 0.2 Multple explaatory varables (0.) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (0.2) Exam 2 Re- grades Re-
Mean is only appropriate for interval or ratio scales, not ordinal or nominal.
Mea Same as ordary average Sum all the data values ad dvde by the sample sze. x = ( x + x +... + x Usg summato otato, we wrte ths as x = x = x = = ) x Mea s oly approprate for terval or rato scales, ot
L5 Polynomial / Spline Curves
L5 Polyomal / Sple Curves Cotets Coc sectos Polyomal Curves Hermte Curves Bezer Curves B-Sples No-Uform Ratoal B-Sples (NURBS) Mapulato ad Represetato of Curves Types of Curve Equatos Implct: Descrbe a
Simple Linear Regression
Correlato ad Smple Lear Regresso Berl Che Departmet of Computer Scece & Iformato Egeerg Natoal Tawa Normal Uversty Referece:. W. Navd. Statstcs for Egeerg ad Scetsts. Chapter 7 (7.-7.3) & Teachg Materal
Lecture Notes Types of economic variables
Lecture Notes 3 1. Types of ecoomc varables () Cotuous varable takes o a cotuum the sample space, such as all pots o a le or all real umbers Example: GDP, Polluto cocetrato, etc. () Dscrete varables fte
1 Onto functions and bijections Applications to Counting
1 Oto fuctos ad bectos Applcatos to Coutg Now we move o to a ew topc. Defto 1.1 (Surecto. A fucto f : A B s sad to be surectve or oto f for each b B there s some a A so that f(a B. What are examples of
Point Estimation: definition of estimators
Pot Estmato: defto of estmators Pot estmator: ay fucto W (X,..., X ) of a data sample. The exercse of pot estmato s to use partcular fuctos of the data order to estmate certa ukow populato parameters.
Non-degenerate Perturbation Theory
No-degeerate Perturbato Theory Proble : H E ca't solve exactly. But wth H H H' H" L H E Uperturbed egevalue proble. Ca solve exactly. E Therefore, kow ad. H ' H" called perturbatos Copyrght Mchael D. Fayer,
THE ROYAL STATISTICAL SOCIETY GRADUATE DIPLOMA
THE ROYAL STATISTICAL SOCIETY EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA PAPER II STATISTICAL THEORY & METHODS The Socety provdes these solutos to assst caddates preparg for the examatos future years ad for
Lecture 2 - What are component and system reliability and how it can be improved?
Lecture 2 - What are compoet ad system relablty ad how t ca be mproved? Relablty s a measure of the qualty of the product over the log ru. The cocept of relablty s a exteded tme perod over whch the expected
Lecture 2: Linear Least Squares Regression
Lecture : Lear Least Squares Regresso Dave Armstrog UW Mlwaukee February 8, 016 Is the Relatoshp Lear? lbrary(car) data(davs) d 150) Davs$weght[d]
Module 1 : The equation of continuity. Lecture 5: Conservation of Mass for each species. & Fick s Law
Module : The equato of cotuty Lecture 5: Coservato of Mass for each speces & Fck s Law NPTEL, IIT Kharagpur, Prof. Sakat Chakraborty, Departmet of Chemcal Egeerg 2 Basc Deftos I Mass Trasfer, we usually
{ }{ ( )} (, ) = ( ) ( ) ( ) Chapter 14 Exercises in Sampling Theory. Exercise 1 (Simple random sampling): Solution:
Chapter 4 Exercses Samplg Theory Exercse (Smple radom samplg: Let there be two correlated radom varables X ad A sample of sze s draw from a populato by smple radom samplg wthout replacemet The observed
SUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION do:1.138/ature18636 Aalyss of aobody allostery Cooperatvty, allostery ad coformatoal chages. There are two seemgly cosstet deftos 1 of allostery. Oe s eergy couplg betwee two
Chapter 3 Sampling For Proportions and Percentages
Chapter 3 Samplg For Proportos ad Percetages I may stuatos, the characterstc uder study o whch the observatos are collected are qualtatve ature For example, the resposes of customers may marketg surveys
EECE 301 Signals & Systems
EECE 01 Sgals & Systems Prof. Mark Fowler Note Set #9 Computg D-T Covoluto Readg Assgmet: Secto. of Kame ad Heck 1/ Course Flow Dagram The arrows here show coceptual flow betwee deas. Note the parallel
2.28 The Wall Street Journal is probably referring to the average number of cubes used per glass measured for some population that they have chosen.
.5 x 54.5 a. x 7. 786 7 b. The raked observatos are: 7.4, 7.5, 7.7, 7.8, 7.9, 8.0, 8.. Sce the sample sze 7 s odd, the meda s the (+)/ 4 th raked observato, or meda 7.8 c. The cosumer would more lkely
Rademacher Complexity. Examples
Algorthmc Foudatos of Learg Lecture 3 Rademacher Complexty. Examples Lecturer: Patrck Rebesch Verso: October 16th 018 3.1 Itroducto I the last lecture we troduced the oto of Rademacher complexty ad showed
THE ROYAL STATISTICAL SOCIETY 2016 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 5
THE ROYAL STATISTICAL SOCIETY 06 EAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 5 The Socety s provdg these solutos to assst cadtes preparg for the examatos 07. The solutos are teded as learg ads ad should
Lecture 8: Linear Regression
Lecture 8: Lear egresso May 4, GENOME 56, Sprg Goals Develop basc cocepts of lear regresso from a probablstc framework Estmatg parameters ad hypothess testg wth lear models Lear regresso Su I Lee, CSE
Chapter 9 Jordan Block Matrices
Chapter 9 Jorda Block atrces I ths chapter we wll solve the followg problem. Gve a lear operator T fd a bass R of F such that the matrx R (T) s as smple as possble. f course smple s a matter of taste.
CIS 800/002 The Algorithmic Foundations of Data Privacy October 13, Lecture 9. Database Update Algorithms: Multiplicative Weights
CIS 800/002 The Algorthmc Foudatos of Data Prvacy October 13, 2011 Lecturer: Aaro Roth Lecture 9 Scrbe: Aaro Roth Database Update Algorthms: Multplcatve Weghts We ll recall aga) some deftos from last tme:
18.657: Mathematics of Machine Learning
8.657: Mathematcs of Mache Learg Lecturer: Phlppe Rgollet Lecture 3 Scrbe: James Hrst Sep. 6, 205.5 Learg wth a fte dctoary Recall from the ed of last lecture our setup: We are workg wth a fte dctoary
Can we take the Mysticism Out of the Pearson Coefficient of Linear Correlation?
Ca we tae the Mstcsm Out of the Pearso Coeffcet of Lear Correlato? Itroducto As the ttle of ths tutoral dcates, our purpose s to egeder a clear uderstadg of the Pearso coeffcet of lear correlato studets
Arithmetic Mean and Geometric Mean
Acta Mathematca Ntresa Vol, No, p 43 48 ISSN 453-6083 Arthmetc Mea ad Geometrc Mea Mare Varga a * Peter Mchalča b a Departmet of Mathematcs, Faculty of Natural Sceces, Costate the Phlosopher Uversty Ntra,
ESS Line Fitting
ESS 5 014 17. Le Fttg A very commo problem data aalyss s lookg for relatoshpetwee dfferet parameters ad fttg les or surfaces to data. The smplest example s fttg a straght le ad we wll dscuss that here
Statistics of Random DNA
Statstcs of Radom DNA Aruma Ray Aaro Youg SUNY Geeseo Bomathematcs Group The Am To obta the epectato ad varaces for the ethalpy chage ΔH, etropy chage ΔS ad the free eergy chage ΔG for a radom -mer of
Entropy ISSN by MDPI
Etropy 2003, 5, 233-238 Etropy ISSN 1099-4300 2003 by MDPI www.mdp.org/etropy O the Measure Etropy of Addtve Cellular Automata Hasa Aı Arts ad Sceces Faculty, Departmet of Mathematcs, Harra Uversty; 63100,
ENGI 4421 Propagation of Error Page 8-01
ENGI 441 Propagato of Error Page 8-01 Propagato of Error [Navd Chapter 3; ot Devore] Ay realstc measuremet procedure cotas error. Ay calculatos based o that measuremet wll therefore also cota a error.
b. There appears to be a positive relationship between X and Y; that is, as X increases, so does Y.
.46. a. The frst varable (X) s the frst umber the par ad s plotted o the horzotal axs, whle the secod varable (Y) s the secod umber the par ad s plotted o the vertcal axs. The scatterplot s show the fgure
MA/CSSE 473 Day 27. Dynamic programming
MA/CSSE 473 Day 7 Dyamc Programmg Bomal Coeffcets Warshall's algorthm (Optmal BSTs) Studet questos? Dyamc programmg Used for problems wth recursve solutos ad overlappg subproblems Typcally, we save (memoze)
Lecture 9: Tolerant Testing
Lecture 9: Tolerat Testg Dael Kae Scrbe: Sakeerth Rao Aprl 4, 07 Abstract I ths lecture we prove a quas lear lower boud o the umber of samples eeded to do tolerat testg for L dstace. Tolerat Testg We have
Module 7. Lecture 7: Statistical parameter estimation
Lecture 7: Statstcal parameter estmato Parameter Estmato Methods of Parameter Estmato 1) Method of Matchg Pots ) Method of Momets 3) Mamum Lkelhood method Populato Parameter Sample Parameter Ubased estmato
9 U-STATISTICS. Eh =(m!) 1 Eh(X (1),..., X (m ) ) i.i.d
9 U-STATISTICS Suppose,,..., are P P..d. wth CDF F. Our goal s to estmate the expectato t (P)=Eh(,,..., m ). Note that ths expectato requres more tha oe cotrast to E, E, or Eh( ). Oe example s E or P((,
Simple Linear Regression
Statstcal Methods I (EST 75) Page 139 Smple Lear Regresso Smple regresso applcatos are used to ft a model descrbg a lear relatoshp betwee two varables. The aspects of least squares regresso ad correlato
Lecture 1 Review of Fundamental Statistical Concepts
Lecture Revew of Fudametal Statstcal Cocepts Measures of Cetral Tedecy ad Dsperso A word about otato for ths class: Idvduals a populato are desgated, where the dex rages from to N, ad N s the total umber
Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities
Chemstry 163B Itroducto to Multcompoet Systems ad Partal Molar Quattes 1 the problem of partal mmolar quattes mx: 10 moles ethaol C H 5 OH (580 ml) wth 1 mole water H O (18 ml) get (580+18)=598 ml of soluto?
STK4011 and STK9011 Autumn 2016
STK4 ad STK9 Autum 6 Pot estmato Covers (most of the followg materal from chapter 7: Secto 7.: pages 3-3 Secto 7..: pages 3-33 Secto 7..: pages 35-3 Secto 7..3: pages 34-35 Secto 7.3.: pages 33-33 Secto
h-analogue of Fibonacci Numbers
h-aalogue of Fboacc Numbers arxv:090.0038v [math-ph 30 Sep 009 H.B. Beaoum Prce Mohammad Uversty, Al-Khobar 395, Saud Araba Abstract I ths paper, we troduce the h-aalogue of Fboacc umbers for o-commutatve
Chapter 10 Two Stage Sampling (Subsampling)
Chapter 0 To tage amplg (usamplg) I cluster samplg, all the elemets the selected clusters are surveyed oreover, the effcecy cluster samplg depeds o sze of the cluster As the sze creases, the effcecy decreases
1. A real number x is represented approximately by , and we are told that the relative error is 0.1 %. What is x? Note: There are two answers.
PROBLEMS A real umber s represeted appromately by 63, ad we are told that the relatve error s % What s? Note: There are two aswers Ht : Recall that % relatve error s What s the relatve error volved roudg
is the score of the 1 st student, x
8 Chapter Collectg, Dsplayg, ad Aalyzg your Data. Descrptve Statstcs Sectos explaed how to choose a sample, how to collect ad orgaze data from the sample, ad how to dsplay your data. I ths secto, you wll
A New Family of Transformations for Lifetime Data
Proceedgs of the World Cogress o Egeerg 4 Vol I, WCE 4, July - 4, 4, Lodo, U.K. A New Famly of Trasformatos for Lfetme Data Lakhaa Watthaacheewakul Abstract A famly of trasformatos s the oe of several
3. Basic Concepts: Consequences and Properties
: 3. Basc Cocepts: Cosequeces ad Propertes Markku Jutt Overvew More advaced cosequeces ad propertes of the basc cocepts troduced the prevous lecture are derved. Source The materal s maly based o Sectos.6.8
Linear Regression with One Regressor
Lear Regresso wth Oe Regressor AIM QA.7. Expla how regresso aalyss ecoometrcs measures the relatoshp betwee depedet ad depedet varables. A regresso aalyss has the goal of measurg how chages oe varable,