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### ex2S04

Course: MATH 172, Fall 2009
School: Los Angeles Southwest...
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Word Count: 463

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172 MATH Spring, 2004 Exam #2 Name: There are 100 points. For full credit you must show your work. You may use a calculator, but this does not exempt you from explaining your answers by giving results of computations or sketches of graphs, etc. 1. (36 points) For each model equation, and initial condition, rst give the solution equation. Then answer the other questions. a. Model equation un = (1.07)un1 with...

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172 MATH Spring, 2004 Exam #2 Name: There are 100 points. For full credit you must show your work. You may use a calculator, but this does not exempt you from explaining your answers by giving results of computations or sketches of graphs, etc. 1. (36 points) For each model equation, and initial condition, rst give the solution equation. Then answer the other questions. a. Model equation un = (1.07)un1 with initial condition u0 = 350 ; then . u5 = b. Model equation P (t) = 0.07P (t) with initial contion P (0) = 350 ; then P (5) = . The population is double the initial population when t= . c. Model equation zn = zn1 + (3/2) with initial condition z0 = 9 . d. Model equation vn = 0.96vn1 + 5 with v0 = 200 . Does the equilibrium . Briey explain. appear to be stable (yes or no)? e. In (d) compute the ratio how rapidly vn vn E and explain its signicance by saying vn1 E goes towards or away from the equilibrium. f. (7 bonus points) Model equation P = 0.04P + 5 with P (0) = 200 . 2. (10 points) Verify that Q(x) = 2x2 + cx + d , where c and d are constants, satises the model equation Q (x) = 4 . Compute the values of c and d so that Q(0) = 5 and Q (0) = 3 . 3. (7 points) Convert r = 2 , = 5/6 (radians) to (x, y) coordinates. Also give the equivalent measure of = 5/6 in degrees. . Find A and B so that 4. (10 points) The period of sin(3x) x is = A cos(Bx) has an amplitude of 5 and a period of 4. 5. (12 points) Determine the model equation satised by R(t) = 3 cos 5t + 2 sin 5t . 6. (15 points) Let A = a. 2 2 1.3 0.2 , w= . , v= 1 3 0.15 0.9 Compute Av and Aw . b. The eigenvalues for this matrix are 1 = 1.2 and 2 = 1 , and eigenvectors are v and w . Which goes with which? Briey explain. c. Find a vector that lines up with the eigenvector belonging to eigenvalue 1, but whose column total is 1. 7. (10 points) Compute the sum of each series; or state that no sum exists. k a. k=0 (3/10)(1/5) b. j j=0 (1/4)(5/2) 8. (6 bonus points) In a 2-variable system you nd that eventually un 1.09un1 and vn 1.02vn1 . Is the total population Tn = un + vn growing or decling? Can you say at what rate? Is there eventually a stable distributio...

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Los Angeles Southwest College - MATH - 411
SCCC 411BStudy Guide for Exam #1Fall, 1995Our goal in this course is to get you thinking about models, not cramming information into your heads. Nevertheless there are a few things that are so fundamental that you really should memorize them. M
Los Angeles Southwest College - MATH - 763
SCCC 411BStudy Guide for Exam #1Fall, 1995Our goal in this course is to get you thinking about models, not cramming information into your heads. Nevertheless there are a few things that are so fundamental that you really should memorize them. M
Los Angeles Southwest College - MATH - 411
SCCC 411B Spring, 1997Final ExamName:There are 140 points. Answer all questions. Be sure to supply adequate explanation for your answers. In most of the problems the later parts do not depend heavily on the earlier parts, so dont give up on (c)
Los Angeles Southwest College - MATH - 763
SCCC 411B Spring, 1997Final ExamName:There are 140 points. Answer all questions. Be sure to supply adequate explanation for your answers. In most of the problems the later parts do not depend heavily on the earlier parts, so dont give up on (c)
Los Angeles Southwest College - STAT - 706
Estimability ExampleAn education major wanted to test the ecacy of teaching methods for the division of fractions. Two new methods along with the standard method were studied. Five teachers were trained in all methods and taught a total of twelve cl
Los Angeles Southwest College - STAT - 517
STAT 517: Delwiche/Slaughter Chapter 3HitchcockChapter 3: Working With Your Data*SAS Alert* In this chapter, we will see several examples of SAS at its worst. The &quot;implict&quot; looping of the DATA step makes several operations that would be easy in
Los Angeles Southwest College - STAT - 517
STAT 517: Scatterplot SmoothingGregoScatterplot Smoothing Scatterplot smoothing is an Exploratory Data Analysis method Multiple versions are available Robust methods (lowesslocally weighted scatterplot smoothing) Non-robust methods (loessloc
Los Angeles Southwest College - STAT - 517
Project Report guidelinesThe project reports can include several different formats: a simulation exercise, a data analysis, a demonstration of software features, function/macro writing, or a discussion of a method not studied in class. These topics
Los Angeles Southwest College - STAT - 706
Type III and Type IV Hypotheses ExampleAn education major wanted to test the efficacy of teaching methods for the division of fractions. Two new methods along with the standard method were studied. Five teachers were trained in all methods and taugh
Los Angeles Southwest College - STAT - 706
Type III and Type IV Hypotheses ExampleAn education major wanted to test the ecacy of teaching methods for the division of fractions. Two new methods along with the standard method were studied. Five teachers were trained in all methods and taught a
Los Angeles Southwest College - STAT - 506
Centerpoint Design ExerciseBackground Centerpoint designs add replications at the origin of a factorial design with quantitative factors; e.g., for a 22 design, centerpoints would be added at the design point (0,0). The additional observations at th
Los Angeles Southwest College - STAT - 706
Two-level designs In this exercise, we will focus on the analysis of an unreplicated full factorial twolevel design, typically referred to as a 2k designk factors, all crossed, with two levels each. I had discussed replicated designs as well, but unr
Los Angeles Southwest College - STAT - 706
Orthogonal and Non-orthogonal Polynomial Constrasts We had carefully reviewed orthogonal polynomial contrasts in class and noted that Brian Yandell makes a compelling case for nonorthogonal polynomial contrasts. In the following example, we will revi
Los Angeles Southwest College - STAT - 706
Review of Completely Randomized Designs Respond to the following questions individually then discuss your answers as a group. You should hand in your individual response. We will discuss your group responses and then I will lecture on other topics. T
Los Angeles Southwest College - STAT - 517
STAT 517/J517 SYLLABUS Spring 2007John M. Grego TTh 11:00-12:15 Wardlaw 116 Oce Hrs: MW 2:30-4:00 200F Leconte 777-5110 grego@stat.sc.eduText The Little SAS Book: A Primer; 3rd Edition, by Delwiche and Slaughter. Supplementary material includes Ba
Los Angeles Southwest College - STAT - 517
STAT 517: Delwiche/Slaughter Chapter 6HitchcockChapter 6: Modifying and Combining Data Sets The SET statement is a powerful statement in the DATA step. Its main use is to read in a previously created SAS data set (either in WORK oranother lib
Los Angeles Southwest College - STAT - 517
STAT 517: Delwiche/Slaughter Chapter 4Hitchcock/GregoChapter 4: Sorting, Printing, Summarizing PROC statements have required statements and optional statements.Example:PROC . . . DATA = . . .; This DATA statement is optional; it species wh
Los Angeles Southwest College - STAT - 517
STAT 517: Delwiche/Slaughter Chapter 7Hitchcock/GregoChapter 7: Macros in SAS Macros provide for more flexible programming in SAS. Macros make SAS more &quot;object-oriented,&quot; like R. In some ways macros serve similar purposes as functions in R.1
Los Angeles Southwest College - STAT - 517
Class Exercise 9This exercise is based upon Chapter 7 of Delwiche and Slaughters The Little SAS book. We will study two dierent macros here. Take your time and be sure you understand every step; be sure to look at intermediate data sheets in the WOR
Los Angeles Southwest College - STAT - 517
STAT 517: Delwiche/Slaughter Chapter 1Hitchcock/GregoChapter 1: Introduction to SAS SAS programs: A sequence of statements in a particular order.Rules for SAS statements: 1. Every SAS statement ends in a semicolon!; 2. Upper/lower case does no
Los Angeles Southwest College - STAT - 706
STATISTICS 706 SYLLABUS Fall 2005John M. Grego MW 4-5:15 BA 204 Oce Hrs: MW 2:30-4:00 200F Leconte 777-5110 grego@stat.sc.eduText Lecture Notes and Design and Analysis of Experiments, Sixth Edition by Douglas C. Montgomery Attendance Though attend
Los Angeles Southwest College - STAT - 517
STAT 517: Delwiche/Slaughter Chapter 2Hitchcock/GregoChapter 2: Getting Data Into SAS Data stored in many different forms/formats. Four categories of methods to read in data.1. Entering data directly through keyboard (small data sets) 2. Crea
Los Angeles Southwest College - STAT - 740
Project Report guidelines The project reports can include several different formats: a simulation exercise, a data analysis, a discussion of an on-going debate, a discussion of a method not studied in class. The first and last will be the more typica
Los Angeles Southwest College - STAT - 770
Project Report guidelines The project reports can include several dierent formats: a data analysis, a discussion of an on-going controversy, a discussion of a method not studied in class. The latter will be the more typical form, and that is the form
Los Angeles Southwest College - STAT - 740
STAT 740 Statistical ComputingJohn M. Grego Office Hours MW 1:30-3 grego@stat.sc.edu Room 200F Phone 777-5110Text and Supplementary Resources. There is no required text, but Monte Carlo Statistical Methods by Robert and Casella covers many topics
Los Angeles Southwest College - STAT - 770
Oral Report guidelines There is not much time to speak during the oral report; I nd it a good idea to focus on one or two of your most interesting elements rather than rush through a comprehensive presentation of your entire report. If you feel you m
Los Angeles Southwest College - STAT - 740
Oral Report guidelines There is not much time to speak during the oral report; I nd it a good idea to focus on one or two of your most interesting topics rather than rush through a comprehensive presentation of your entire report. Do not worry if the
Los Angeles Southwest College - STAT - 517
Ch 11 Graphicsq Managing graphics windows q 1-d, 2-d and 3-d plotting q Interactive graphics Fall 2004 Don Edwards and the University of South Carolina1R graphicsq High level of functionality q Like SAS/Graph, number of options can be intimida
Los Angeles Southwest College - STAT - 517
Ch 12 Function writingq Inputting functions q Function writing examplesqPooled t-test qPlotting Fall 2004 Don Edwards and the University of South Carolina1Inputting functionsq Work from a text file q Fixing and sourcing q Re-editing2Poole
Los Angeles Southwest College - STAT - 506
I.2 Examples To Illustrate DOE Conceptst t1. Optimally Feeding Fish 2. Targeting A Process/Reducing Process Variation 3. Improving A Process 4. Weighing Two Objects 5. Baking Bread 6. Mitigating Noise Factors 7. Comparing Tires Sony USA ve
Los Angeles Southwest College - STAT - 740
Notes on Kernel Density EstimationThe R function density handles most of the estimation approaches we studied in class. R also has a library (KernSmooth) of kernel density functions, but it seemed a bit piecemeal and outdated. We can load the datase
Los Angeles Southwest College - STAT - 506
I.4 Implementation Issuest tFundamentals of Problem Solving DOE Implementation Issues DOE Stages Helicopter Experiment Project ReportstProblem Solving/DOELevels of UnderstandingI.4.1The Center for Reliabilty and Quality Sciences Depart
Los Angeles Southwest College - STAT - 506
I.5 Taguchi's Philosophyt t t t tSome Important Aspects Loss Functions Exploiting Nonlinearities Examples Taguchi Comments and Criticisms5.1The Center for Reliabilty and Quality Sciences Department of Statistics The University of South Carolin
Los Angeles Southwest College - STAT - 706
Designs with Randomization Restrictions RCBD with a complete factorial in each block A: Cooling Method B: Temperature Conduct ab experiments in each blockDesigns with Randomization Restrictions All factors are crossedYijk = + i + j + ij
Los Angeles Southwest College - STAT - 706
Population Marginal Means Two factor model with replication Yijk = ij + ijk , k = 1, , nij Yijk nijYij. j k j Yi. = = nij nijn E (Y ) = nij j i . ij jjjij~ = i.Population Marginal MeansE (Yi. ) = E (Y. j . ) = E (Y. ) =n ij j
Los Angeles Southwest College - STAT - 706
Resource Allocation Given N observations, how should we allocate them to a treatments?Minimize V (Y ) subject to N = ni. 1 1aai Use a Lagrange multiplier and minimizea N -n F= + i 1 ni 1 a 2Resource AllocationF =- 2 -=0 ni ni
Los Angeles Southwest College - STAT - 706
Nested Designs Ex 1-Compare 4 states' low-level radioactive hospital waste A: State B: Hospital Rep: Daily wasteNested Designs Ex 2-Compare tobacco yield/acre in 5 counties A: County B: Farm Rep: Field Yield/acre Other Ex-Tick study, Clas
Los Angeles Southwest College - STAT - 706
Estimability Effects model:Yij = i + ij = + i + ij , j = 1, , n i = i - Linear combinations of parameters are estimable only if they can be expressed as linear combinations of the cell means { i}Estimability Linear combinations of cell
Los Angeles Southwest College - STAT - 770
data crab;input color spine width satell weight; if satell=0 then bisat=0; else bisat=1; weight=weight/1000; cards;3 3 28.3 8 30504 3 22.5 0 15502 1 26.0 9 23004 3 24.8 0 21004 3 26.0 4 26003 3 23.8 0 21002 1 26
Los Angeles Southwest College - STAT - 519
StateRegion1991199019802010AreaPopDens MedAge&lt;18&gt;65SectionMaineNE123512281125145335.440.0134.325.113.41NewHampshireNE1105110992115259.4123.2033.325.311.61VermontNE5675635116549.661.3033.425.611.81Massa
Los Angeles Southwest College - STAT - 519
Here are the commands we used in exploring bounds on the error ofestimation in confidence intervals for a mean collected from a simple random sample in Minitab. To look at the sample size neededover a wide range of choices of B and sigma, we need
Los Angeles Southwest College - STAT - 517
These are various college football scoresfrom early in the 2004 season.The first column is the visiting team, the second the visitor's score,then the home team and their score.The fifth column is a note about the game and the sixth is how much a
Los Angeles Southwest College - STAT - 770
m2logL=function(Lambda){2*Lambda-20-20*log(Lambda/10)-qchisq(.95,1)}Lambda=seq(2,20,by=.5)plot(Lambda,m2logL(Lambda)+qchisq(.95,1),type=&quot;l&quot;,ylab=&quot;-2logL&quot;)abline(h=qchisq(.95,1)uniroot(m2logL,interval=c(3,10)\$rootuniroot(m2logL,interval=c(10,25)\$
Los Angeles Southwest College - STAT - 506
macro rse x1 x2 ymcolumn x1 x2 y zmconstant nrandlet nrand=count(x1)rand nrand z;normal 0 .6.let y=18.5+2.376*x1+1.2*x2-.0234375*x1*x1-.02*x2*x2+.0125*x1*x2+zendmacro
Los Angeles Southwest College - STAT - 517
Maalea sail sch 75.00 Maalea sail yac 32.95 Lahaina sail cat 62.00 Maalea power cat 22.00 Maalea sail sch 47.50 Maalea power cat 28.99 Maalea power y
Los Angeles Southwest College - STAT - 770
Final Exam 1. A researcher is testing the use of three different formats for the same product: Print, Online, CD. Respondents indicated their use of the product on an ordinal scale (1=Never, 2=Rarely, 3=Sometimes, 4=Often/Always). The data is availab
Los Angeles Southwest College - STAT - 740
Markov Chain Monte Carlo ExerciseIn this exercise, we will study an implementation of the Metropolis-Hastings algorithm for the Ising model, and work with BRugs on selected machines on which it has been downloaded. I would encourage you to study BRu
Los Angeles Southwest College - STAT - 740
Reading a function into RThe R function buffon is available on the website as a text le. The le actually names the function: buffon=function(n,l,p){ . . . } We use the source command to read the le. We do not have to use an R assignment (= or &lt;-) to
Los Angeles Southwest College - STAT - 770
Section 3.4 Computer Exercise1. We will be working with the Hog data; copy the SAS program (listed as Chapter 2 contingency table on the webpage) into SAS. Add CMH1 as an option to the TABLES command to obtain the M 2 statistic for the default score
Los Angeles Southwest College - STAT - 740
Calling Fortran Subroutines in R on a PCRefer to Brian Habings webpage for downloading and installing Fortran from the MinGW website. The material presented here is consistent with the portion of Brians website that deals with running Fortran subrou
Los Angeles Southwest College - STAT - 740
Bootstrap ExerciseSome nonparametric bootstrap condence interval techniques are suciently easy to implement that you should consider writing your own. Working with the breast cancer data, we can construct 95% condence intervals for the 25% trimmed m
Los Angeles Southwest College - STAT - 706
Midterm 1. In a Complete Randomized Design, 7 dierent levels of baking powder were tested for their eect on relative rise of biscuit dough. 4 biscuits were baked using each recipe. Use = .05 for all tests. (a) Test the cell means model and examine t
Los Angeles Southwest College - STAT - 517
STAT 517: Final ExamProvide code, output, and answers in either Word, PDF, RTF, or text format; try to combine les as much as possible before sending them to me. Work independently. 1. A hostess at a restaurant recorded tips received each day over t
Los Angeles Southwest College - STAT - 517
STAT 517: AppendicesHitchcockGregoSAS and other packages SAS can interact with other packages in a variety of different ways. We will brieydiscuss SPSSX SUDAAN IML SQL will be discussed in more detailUniversity of South CarolinaPage 1
Los Angeles Southwest College - STAT - 706
Homework 1 1. For the data in Problem 3.36, use orthogonal polynomial contrasts to test whether or not a linear model is better than an intercept model; whether or not a quadratic model (with a linear term) is better than an intercept model. Are eith
Los Angeles Southwest College - STAT - 706
Homework 1 1. For the following data, use orthogonal polynomial contrasts to test whether or not a linear model is better than an intercept model; whether or not a quadratic model (with a linear term) is better than an intercept model. Are either of
Los Angeles Southwest College - STAT - 770
Midterm Exam 1. Consider the following 2X2 table with xed row and column marginals: 12 3 15 (a) What is the range of n11 ? (b) Consider the exact test of Ho : = 2 vs. HA : &gt; 2 ( = .05). Find the rejection region and compute a p-value for this test.
Los Angeles Southwest College - STAT - 706
Latin Square Design Traditionally, latin squares have two blocks, 1 treatment, all of size n Yandell introduces latin squares as an incomplete factorial design instead Though his example seems to have at least one block (batch) Latin squares hav
Los Angeles Southwest College - STAT - 706
Chapter coverage Part A 1: Practical tools 2: Consulting 3: Design Principles Part B (4-6) One-way ANOVA Part C (7-9) Factorial CRD Part D (10-12) Unbalanced CRDChapter coverage Part E (13-15) Questioning Assumptions Part F (16-18) ANC
Los Angeles Southwest College - QARTOD - 3
Quality Assurance of Real-Time Oceanographic Data (QARTOD III)Scripps Institution of Oceanography, La Jolla, CA November 2-4, 2005Day 1 (Wednesday, November 2, 2005)Time 7:30 - 8:30am 8:30 8:45 8:45 9:15 Topic Continental Breakfast/Registration
Los Angeles Southwest College - QARTOD - 4
QARTOD IV AgendaFourth Workshop on the QC/QA of Real-Time Oceanographic Data June 21 - 23, 2006Woods Hole Oceanographic Institution Clark 507/Quissett Campus WEDNESDAY - JUNE 21, 20067:30 - 8:30 8:30-9:20 REGISTRATION &amp; CONTINENTAL BREAKFAST INTR