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Course: MCS 441, Fall 2008
School: Ill. Chicago
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Ill. Chicago - MCS - 441
1 Solution to extra credit 1.57 Let M be a DFA for A. In the following, we assume that the alphabet of A is {0, 1}. Dene the NFA N for A1/2 in the following way. For every state p of M , let Mp start at p and work like M , but instead of reading its
Ill. Chicago - MCS - 441
Midterm Exam for MCS 441: Theory of Computation I March 3, 2007 1) Construct an NFA which accepts the language of words over {0, 1} whose number of 1's is not divisible by three. 2) Find an RE which generates the language of words over { , } which st
Ill. Chicago - MCS - 441
Solutions to Midterm Exam 1) ONML 1 ONML HIJK HIJK G 0 G 1 bb bb bb 1 1 bb b ONML HIJK 2 y G G0 0 02) where = 3) .ONML 0 G GFED HIJK @ABC c b y 0 1 G GFED @ABC a 1 ,@ABC G GFED s@ABC G GFED s @ABC G GFED s G GFED @A
Ill. Chicago - MCS - 441
230A. M. TUKING[Nov.12,ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEMBy A. M. TURING. [Received 28 May, 1936.-Read 12 November, 1936.]The &quot;computable&quot; numbers may be described briefly as the real numbers whose expre
Ill. Chicago - MCS - 441
An Unsolvable Problem of Elementary Number Theory Alonzo Church American Journal of Mathematics, Vol. 58, No. 2. (Apr., 1936), pp. 345-363.Stable URL: http:/links.jstor.org/sici?sici=0002-9327%28193604%2958%3A2%3C345%3AAUPOEN%3E2.0.CO%3B2-1 American
UMass (Amherst) - RESEC - 312
Name: Exam 1A KeyLab Exam 1A Univariate and Bivariate Statistics The spreadsheet Exam 1A 2009 contains a sample of used 2004 Honda Accord prices and related data. Before you do anything, save your file to the folder named &quot;Dropbox&quot; as: Exam 1A las
Ill. Chicago - MCS - 441
HW8 Mar 10 Problem 1 (a) (, qs , ) (, qr , ) because, by convention, (qs , ) = (qr , , S). (b) (, qs , 10#10) (x, q2 , 0#10) (x0, q2 , #10) (x0#, q4 , 10) (x0#x, q5 , 0) (x0#, q6 , x0) (x0, q6 , #x0) (x, q7 , 0#x0) (, q7 , x0#x0) (x, qs , 0
UMass (Amherst) - RESEC - 312
Key - Exam 2A Please use the data set Exam2 Demand for Money.xls for all analyses. Variables in the Excel spreadsheet are for the years 1960-1983 and are defined as follows: GNP the U.S. Gross National Product in billions of dollars. M1 U.S. deman
UMass (Amherst) - RESEC - 312
Year 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 Means Medians St. Dev.M1 141.8 146.5 149.2 154.7 161.8 169.5 173.7 185.1 199.4 205.8 216.5 230.7 251.9 265.8 277.5 291.1 31
Ill. Chicago - MCS - 441
UMass (Amherst) - RESEC - 312
Exam 3Resource Economics 312 Introductory EconometricsPlease complete all questions on this exam. The data in the spreadsheet: Exam 3- Wages.xls are to be used for all analyses. These data are a sample of 2004 New England private wage earners. Th
UMass (Amherst) - RESEC - 312
Lab 1: Organizing and Describing Data Objectives: 1. Introduce Excel as a tool for organizing and analyzing data. 2. Practice manipulating data. 3. Review Organizing Data from basic stats use Excel to illustrate frequency and relative frequency dist
Missouri S&T - MATH - 2051
ee ee ee ee ee ee ee ee | | |f | |k ~ l t nPVVnv|IGAcVh|E3EnqhEG0 v v o o o } v s v } v v o '5VvnvpfG|T3GfqVAhEIeuupGuEAgV|'dg|yXnAf3ACoupAXVdnxE3kEGu!cph o v v o
UMass (Amherst) - RESEC - 312
Distribution of Used 2004 Honda Accord Prices Accord Prices Frequency Relative Frequency Less than \$15,000 You You \$15,000 &lt; \$16,000 need need \$16,000 &lt; \$17,000 counts relative \$17,000 &lt; \$18,000 for frequencies \$18,000 &lt; \$19,000 each for \$19,000 &lt; \$2
Ill. Chicago - MCS - 441
1 HW11 Extra credit: problem 4.17 Let D be a decidable language over alphabet {#}, where # . Consider C = {x : y such that x#y D}. Let M be the TM which decides D. The TM N which recognizes C does the following. Input: x . Output: Accept, i
UMass (Amherst) - RESEC - 312
Distribution of Used 2004 Honda Accord Prices Accord Prices Frequency Relative Frequency Less than \$15,000 2 0.020 \$15,000 &lt; \$16,000 0 0.000 \$16,000 &lt; \$17,000 2 0.020 \$17,000 &lt; \$18,000 9 0.090 \$18,000 &lt; \$19,000 10 0.100 \$19,000 &lt; \$20,000 14 0.140 \$20
UMass (Amherst) - RESEC - 312
Lab 3: The Sampling Distribution, Interval Estimation, Correlation and CovarianceObjectives: 1. Complete an example of a t-test, or two. 2. Still more practice with Excel: equations and functions. 3. Bivariate distributions relationship between two
UMass (Amherst) - RESEC - 312
Covariance and Correlation:Covariance and correlation measure linear association between two variables, say X and Y.Covariance:Population Parameter: X ,Y = (Y iY)( X i X )NThe population parameter describes linear association betw
UMass (Amherst) - RESEC - 312
Excel Functions: + * ^Syntax =C5+D5 =C5-D5 =C5*D5 =C5^2Definition/Description Adds the values found in cells C5 and D5. Subtracts . Multiplies . Creates the square of the value in C5. The dollar sign locks cell addresses so that they do not chang
UMass (Amherst) - RESEC - 312
Excel Functions: + * ^Syntax =C5+D5 =C5-D5 =C5*D5 =C5^2Definition/Description Adds the values found in cells C5 and D5. Subtracts Multiplies Creates the square of the value in C5. The dollar sign locks cell addresses so that they do not change
UMass (Amherst) - RESEC - 312
DATE Bonds (Aaa) 1976 8.43 1977 8.02 1978 8.73 1979 9.63 1980 11.94 1981 14.17 1982 13.79 1983 12.04 1984 12.71 1985 11.37 1986 9.02 1987 9.38 1988 9.71 1989 9.26 1990 9.32 1991 8.77 1992 8.14 1993 7.22 1994 7.97 1995 7.59 1996 7.37 1997 7.27 1998 6.
UMass (Amherst) - RESEC - 312
Name: Lab Exam 1A - Distributions of DataOpen the Excel spreadsheet: Exam 1A found in the course folder. The Excel file contains a sample of Amherst home sales; the sample was collected for the year 2003. Complete the exercises below using these sam
UMass (Amherst) - RESEC - 312
Address 18 Trillium Way 52 Elf Hill Rd L2 Kestrel Ln Lot 25 Hop Brook Rd 26 Teaberry Ln L20 Hop Brook Rd 3 Bayberry Ln 585 Station Rd 30 Bridle Path 27 Woodlot Rd 23 Alyssum Dr Lot1 Arbor Way L42 WoodLot 1050 Bay Rd 45 Hills Rd 45 Phillips St 293 Bel
UMass (Amherst) - RESEC - 312
Address 234 Henry St 293 Belchertown Rd 143 South East St 34 Logtown Rd 340 Amity St 45 Phillips St 52 Elf Hill Rd 1299 Bay Rd 1050 Bay Rd 15 Cortland Dr 585 Station Rd Lot1 Arbor Way 30 Bridle Path 217 Aubinwood Rd 83 N Prospect St 18 Trillium Way 4
UMass (Amherst) - RESEC - 312
Lab 5: OLS Live and RegressionObjectives: 1. Review OLS. What does OLS mean? What does it accomplish? What do we choose? 2. Create a spreadsheet including the data manipulations needed to estimate a regression line. 3. Given sample data, use Excel t
UMass (Amherst) - RESEC - 312
X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23E[Y] 21.5 32 41.5 50 57.5 64 69.5 74 77.5 80 81.5 82 81.5 80 77.5 74 69.5 64 57.5 50 41.5 32 21.5u -3.22 -3.9 2.25 4.95 2.22 6.85 -2.77 -1.66 -0.49 5.09 -3.27 -4.01 1.71 -0.41 -2.76 -0.
UMass (Amherst) - RESEC - 312
Lab 6: Sampling Distributions for OLS EstimatorsObjectives: ^ ^ The OLS estimators 0 and 1 are random variables they have sampling distributions. In order to proceed from point estimation to interval estimation, we need to know about the sampling
Ill. Chicago - MCS - 441
1 HW12 1. a) f (0) = 0, f (1) = 1, f (2) = 1, f (3) = 0. b) 0, if n is even, f (n) = 1, otherwise. c) f (0) = 100, f (1) = 1000, f (2) = 10000. d) f (n) = n3 + n. 2. Let M = {x0 , . . . , xm-1 } and N = {y0 , . . . , yn-1 }. For k {0, . . . , nm -
UMass (Amherst) - RESEC - 312
Name: Random Seeds X 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 195 E[Y|X] u1 u2 Y1 Y2 x x-sq xY1 xY2Sample 1 Results: beta 0 hat: beta 1 hat: Sample 2 Results: beta 0 hat: beta 1 hat:sigma beta 1 hat:90% Co
UMass (Amherst) - RESEC - 312
Lab 7: Regression Topics: Confidence Intervals, Plots and Non-Linear ModelsObjectives: We now assume that the mean of our dependent variable changes as the independent variable changes: E[ Y X t ] = 0 + 1 X t . The primary objectives for this lab a
UMass (Amherst) - RESEC - 312
Year 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966W 1.62 1.65 1.79 1.94 2.03 2.12 2.26 2.44 2.57 2.66 2.73 2.8 2.92 3.02 3.13 3.28 3.43 3.58wdotU 1 1.4 1.1 1 1.5 1.2 1 1.1 1.3 1.8 1.9 1.5 1.4 1.8 1.1
UMass (Amherst) - RESEC - 312
Year 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966W 1.62 1.65 1.79 1.94 2.03 2.12 2.26 2.44 2.57 2.66 2.73 2.8 2.92 3.02 3.13 3.28 3.43 3.58wdotU 1 1.4 1.1 1 1.5 1.2 1 1.1 1.3 1.8 1.9 1.5 1.4 1.8 1.1
UMass (Amherst) - RESEC - 312
Year 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966W 1.62 1.65 1.79 1.94 2.03 2.12 2.26 2.44 2.57 2.66 2.73 2.8 2.92 3.02 3.13 3.28 3.43 3.58wdotU 1 1.4 1.1 1 1.5 1.2 1 1.1 1.3 1.8 1.9 1.5 1.4 1.8 1.1
UMass (Amherst) - RESEC - 312
Lab 8: Multiple Regression: Excel and MinitabObjectives: We all agree that most economic models would require estimation of a multiple regression. The objective of todays lab is to estimate multiple regression models in Excel and introduce you to da
UMass (Amherst) - RESEC - 312
year 1971 1971 1972 1972 1972 1972 1973 1973 1973 1973 1974 1974 1974 1974 1975 1975quarter 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2sales prose pcarn dinc trend 11484 2.26 3.49 158.11 9348 2.54 2.85 173.36 8429 3.07 4.06 165.26 10079 2.91 3.64 172.92 9240
UMass (Amherst) - RESEC - 312
year 1971 1971 1972 1972 1972 1972 1973 1973 1973 1973 1974 1974 1974 1974 1975 1975quarter 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2sales prose 11484 9348 8429 10079 9240 8862 6216 8253 8038 7476 5911 7950 6134 5868 3160 5872pcarn 2.26 2.54 3.07 2.91 2.
Ill. Chicago - MCS - 441
Final Exam for MCS 441: Theory of Computation I May 7, 2008 A perfect score is given for the star problems and any 6 other problems (2+1+1+2). Solving additional problems is to your benefit. Good luck! 1) Write a RE which generates the even length wo
UMass (Amherst) - RESEC - 312
Descriptive Statistics: sales, prose, pcarn, dincVariable sales prose pcarn dinc N 16 16 16 16 Mean 7645 3.107 3.4319 180.53 SE Mean 511 0.134 0.0812 2.47 StDev 2043 0.538 0.3249 9.87 Minimum 3160 2.260 2.8500 158.11 Q1 5967 2.740 3.1475 173.94 Medi
UMass (Amherst) - RESEC - 312
year 1971 1971 1972 1972 1972 1972 1973 1973 1973 1973 1974 1974 1974 1974 1975 1975quarter 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2sales prose pcarn dinc trend 11484 2.26 3.49 158.11 9348 2.54 2.85 173.36 8429 3.07 4.06 165.26 10079 2.91 3.64 172.92 9240
UMass (Amherst) - RESEC - 312
year 1971 1971 1972 1972 1972 1972 1973 1973 1973 1973 1974 1974 1974 1974 1975 1975quarter 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2sales prose 11484 9348 8429 10079 9240 8862 6216 8253 8038 7476 5911 7950 6134 5868 3160 5872pcarn 2.26 2.54 3.07 2.91 2.
UMass (Amherst) - RESEC - 312
Lab Exam 2A Please use the data set Home Prices.xls for all analyses below. The data set can be found in the ResEc 312 folder on the server. The data set includes the following variables: PRICE - the price of the home in dollars. TOWN - the town in w
UMass (Amherst) - RESEC - 312
OBSN HOME 39 96 Avenue F 40 370-42 Mill Valley 41 29 Avenue A 42 L82 Avenue B 43 94 Channel Dr 44 370 Mill Valley Rd #52 45 259 Ave G 46 533 Avenue L 47 162 Amherst Rd 48 638 Federal St 1 228 Henry St 49 622 Federal 2 110 Henry St 3 234 Henry St 50 9
UMass (Amherst) - RESEC - 312
OBSNHOME 1 228 Henry St 2 110 Henry St 3 234 Henry St 4 293 Belchertown Rd 5 143 South East St 6 34 Logtown Rd 7 340 Amity St 8 45 Phillips St 9 154 Summer St 10 295 Amity St 11 52 Elf Hill Rd 12 Lot 1 Old Farm Rd 13 1299 Bay Rd 14 1050 Bay Rd 15 1
UMass (Amherst) - RESEC - 312
Lab Exam 2A Please use the data set Home Prices.xls for all analyses below. The data set can be found in the ResEc 312 folder on the server. The data set includes the following variables: PRICE - the price of the home in dollars. TOWN - the town in w
Ill. Chicago - MCS - 441
Extra credit problem for Feb 11 Show that the language {0m 1n | m, n 0 and m = n} is not regular using directly the pumping lemma.1
UMass (Amherst) - RESEC - 312
OBSNHOME 1 228 Henry St 2 110 Henry St 3 234 Henry St 4 293 Belchertown Rd 5 143 South East St 6 34 Logtown Rd 7 340 Amity St 8 45 Phillips St 9 154 Summer St 10 295 Amity St 11 52 Elf Hill Rd 12 Lot 1 Old Farm Rd 13 1299 Bay Rd 14 1050 Bay Rd 15 1
UMass (Amherst) - RESEC - 312
Lab 9: Dummy Variables and Data ManipulationsObjectives: This lab will introduce you to data manipulations in Minitab, especially the creation of dummy variables and interaction variables. Well then use one of the most common data transformations in
Ill. Chicago - MCS - 441
HW for Mar 10 Write the sequence of congurations which the Turing machine below goes through on the following inputs. Remember that, if the head reads a symbol for which there is no arrow, by convention the machine goes to the rejecting state qr . (a
UMass (Amherst) - RESEC - 312
Lab 10: Data Manipulations and Non-Linear ModelsObjectives: It is not unusual to have to make some modifications to your data before estimation. In the first part of the lab, well use Minitab to do some data manipulations. The second part of the lab
UMass (Amherst) - RESEC - 312
Exam 2 Practice ProblemsIntro. Econometrics Res. Economics 3121. Using the data in the file CPS1985-NonLin.mtw estimate the model(s) required to address the following questions. These are actual survey data collected in 1985 from 534 U.S. citizen
UMass (Amherst) - RESEC - 312
Regression Analysis: wage versus ed, exThe regression equation is wage = - 4.90 + 0.926 ed + 0.105 ex Predictor Constant ed ex Coef -4.904 0.92595 0.10513 SE Coef 1.219 0.08140 0.01720 T -4.02 11.38 6.11 P 0.000 0.000 0.000S = 4.59914R-Sq = 20.2
UMass (Amherst) - RESEC - 312
Lab 11: MulticollinearityObjectives: In todays lab we will investigate the existence of a problem in the sample data - Multicollinearity. Multcollinearity is the existence of linear association among two or more independent variables. The mere exist
UMass (Amherst) - RESEC - 312
year 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982qchik 27.8 29.9 29.8 30.8 31.2 33.3 35.6 36.4 36.7 38.4 40.4 40.3 41.8 40.4 40.7 40.1 42.7 44.1 46.7 50.6 50.1 51.7 52.9dinc 39
UMass (Amherst) - RESEC - 312
Regression Analysis: qchik versus pchik, ppork, pbeef, dincThe regression equation is qchik = 37.2 - 0.611 pchik + 0.198 ppork + 0.0695 pbeef + 0.00501 dinc Predictor Constant pchik ppork pbeef dinc Coef 37.232 -0.6112 0.19841 0.06950 0.005011 SE Co
Ill. Chicago - MCS - 441
HW for Mar 12 1) Write the sequence of configurations which the Turing machine below goes through on the following inputs. Remember that, if the head reads a symbol for which there is no arrow, by convention the machine goes to the rejecting state qr
UMass (Amherst) - RESEC - 312
Name:Exam 1 B (15) Introductory Econometrics Resource Economics 3121. Explain the basic idea behind Dan's OLS Live spreadsheet and the OLS method. In particular: (1) What is the OLS criterion and how is it used in fitting a line? (2) What two thin
Ill. Chicago - MCS - 441
HW for Mar 14 1) Define a busy Turing Machine to be one which never stays, i.e. its transition function has the form : Q Q {L, R} (no S). Show that a language L is recognizable/decidable by a busy TM if and only if it is recognizable/decidable
UMass (Amherst) - RESEC - 312
Exam 2Resource Economics 312 Introductory Econometrics1. Early in this course, Dan uttered his battle cry: &quot;Estimators are random variables!&quot; (4) a. Explain clearly why OLS estimators for the population parameters of a regression model are random
Ill. Chicago - MCS - 441
HW for Mar 17 1) Let b 2 be an integer and let b = {1, 2, . . . , b}. Order the words from in the following way b , 1, 2, . . . , b, 11, 21, . . . , b1, 12, . . . , 22, . . . , 1b, . . . , bb, 111, 211, . . . More precisely we have the following. F
North Texas - BIOL - 1130
Chapter 1This lecture will help you understand: 0. The nature of environmental science 1. Natural resources and their importance 2. The scientific method and the scientific process 3. Pressures on the global environment 4. Sustainability The &quot;enviro
UMass (Amherst) - RESEC - 312
Exam 2 - KeyResource Economics 312 Introductory Econometrics1. Early in this course, Dan uttered his battle cry: &quot;Estimators are random variables!&quot; (4) a. Explain clearly why OLS estimators for the population parameters of a regression model are