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15 Pages

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Course: STAT 511, Fall 2008
School: Purdue
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Word Count: 655

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511: Statistics Statistical Methods Dr. Levine Purdue University Fall 2006 Lecture 9: The Normal Distribution Devore: Section 4.3 Aug, 2006 Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2006 Denition A continuous RV X is said to have a normal distribution with parameters and 2 , < < and 0 < 2 , if the pdf of X is 1 2 (x)2 /2 2 e f (x; , ) = 2 for all...

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511: Statistics Statistical Methods Dr. Levine Purdue University Fall 2006 Lecture 9: The Normal Distribution Devore: Section 4.3 Aug, 2006 Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2006 Denition A continuous RV X is said to have a normal distribution with parameters and 2 , < < and 0 < 2 , if the pdf of X is 1 2 (x)2 /2 2 e f (x; , ) = 2 for all < x < . The normal distribution is very important as it describes a ...
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Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 9: Other Continuous DistributionDevore: Section 4.3Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Gamma Distribution Ga
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 10: Probability PlotsDevore: Section 4.6Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Sample Percentiles For a given p
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 11: Random SamplesDevore: Section 5.3-5.4Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Denition of a Statistic A stati
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 12: Condence IntervalsDevore: Section 7.1-7.2Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Motivation Why do we need a
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 13: Additional Condence Intervals Related TopicsDevore: Section 7.3-7.4Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006t-c
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Midterm2: Practice ProblemsAug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006 By how much must the sample size n be increased if the
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Midterm2: Practice ProblemsAug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006 By how much must the sample size n be increased if the
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 14: Introduction to Hypothesis TestingDevore: Section 8.1Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006What is statistic
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 15: Tests about a Population MeanDevore: Section 8.2Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006A Normal Population wi
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 16: Tests about a Population ProportionDevore: Section 8.3Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Large-Sample Tes
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 17: P-values and some Additional Issues concerning TestingDevore: Section 8.4-8.5Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 18: Inferences Based on Two SamplesDevore: Section 9.1-9.2Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006z Tests and Cond
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 18: Inferences Based on Two SamplesDevore: Section 9.1-9.2Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006z Tests and Cond
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 19: Analysis of Paired DataDevore: Section 9.3Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Analysis of Paired Data Th
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 19: Analysis of Paired DataDevore: Section 9.3Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Analysis of Paired Data Th
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 20: Two Sample Test for Proportions and the Variance TestDevore: Section 9.4-9.5Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Lecture 20: Lecture 20: Two Sample Test for Proportions and the Variance TestDevore: Section 9.4-9.5Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue Univ
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Practice Problems for the Final Exam, Fall 2006Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Example 1 Consider a new design fo
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Practice Problems for the Final Exam, Fall 2006Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Example 1 Consider a new design fo
Purdue - STAT - 511
HOMEWORK 11.10 a. Minitab generates the following stem-and-leaf display of this data: 59 6 33588 7 00234677889 8 127 9 077 stem: ones 10 7 leaf: tenths 11 368 What constitutes large or small variation usually depends on the application at hand, but
Purdue - STAT - 511
Stat 511 Homework #2 Section 2.1: 9; 2.2: 13, 18, 22; 2.3: 39, 44; 2.4: 589: (a) ( A B)' = A' B'( A B )' - shaded area (red)A shaded area (blue) B striped area A' B ' - area both shaded blue and striped(b) ( A B )' = A' B 'AB=AB
Purdue - STAT - 511
Stat 511 Homework #3 Solutions Section 2.5: Pr. 71, 76. Section 3.1: Pr. 4. Section 3.2: Pr. 12, 18, 23 Section 3.3: Pr. 32, 35. 2.71 P ( A B ) = P ( B ) P ( A B ) = P ( B ) P( A) P ( B ) = [1 P ( A)] P ( B ) = P ( A) P ( B )Alternatively,
Purdue - STAT - 511
Stat 511 Homework #4 Solution Section 3.4: 51, 56, 59; 3.6: 77, 79, 86; Additional Problem51: Given: 20% of all telephones of a certain type are submitted for service while under warranty. Of those, 60% can be repaired, whereas the other 40% must be
Purdue - STAT - 511
Stat 511 Homework #5 Solution Section 4.1: Pr. 3, 5, 10, Section 4.2: Pr. 12, 18, 21, 23, Section 4.3: Pr. 27, 29, 33 3. a) Graph of f(x) = .09375(4 x2)x3 b) P(X &gt; 0) = .09375(4 x )dx = .09375(4 x ) = .5 0 3 02 22c) P(-1 &lt; X &lt; 1) =1
Purdue - STAT - 511
Homework # 6 Stat 511- Fall 2006
Purdue - STAT - 511
Stat 511 Homework #7 Solution Section 5.4: Pr. 48, 50, Section 7.1: Pr. 1, 3, 7, Section 7.2: Pr. 12, 15, 20 Section 5.4 48.a. X = = 50 , x =x 1 = = .10 n 10050.25 50 49.75 50 Z .10 .10 P( 49.75 X 50.25) = P = P(-2.5 Z 2.5) = .987
Purdue - STAT - 511
Stat 511 Homework #8 Section 8.1: 1, 7, 9 ;Section 8.2: 15, 16, 19, 21
Purdue - STAT - 511
Stat 511 Homework #9 Solution (Section 8.3: Pr. 35, 37, 41, Section 8.4: Pr. 45, 46, 49, 55) Section 8.3 35.1 Parameter of interest: p = true proportion of cars in this particular county passing emissions testing on the first try. Ho: p = .70 Ha: p
Purdue - STAT - 511
Problem 1 (5pt) We must find P( Pj | D) for j = 1,2,3 . Bayes rule gives us P ( P1 | D) = P ( P1 ) P ( D | P1 ) = 0.3 0.01 = 0.158 0.3 0.01 + 0.2 0.03 + 0.5 0.02 0.2 0.03 = 0.316 0.3 0.01 + 0.2 0.03 + 0.5 0.02 0.5 0.02 = 0.526 0.3 0.01 + 0.
Purdue - STAT - 511
MIDTERM 2 STAT 511, FALL 2006 Total is 20pt Problem 1 (5pt) Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows:x p(x)1 .42 .33 .24 .1a.
Purdue - STAT - 511
Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Practice ProblemsDevore: Chapters 1-3Aug, 2006Statistics 511: Statistical Methods Dr. LevinePurdue University Fall 2006Chapter 1, Pr. 22 A very large percentage o
Purdue - STAT - 520
STAT 520 TIME SERIES AND APPLICATIONSPROF. MICHAEL LEVINE Tel. (office) 765-496-7571 E-mail mlevins@stat.purdue.edu CLASS MEETING TIME AND PLACE: TTh, 3.00-4.15pm, UNIV 217 Office hours: TTh, 2-3pm, HAAS 154 or by appointment THE COURSE WEBPAGE IS
Purdue - STAT - 520
Testing the estimated noise sequence. 20pt 1. We know the classical result that states the sample autocorrelations of an iid sequence Y1 , . . . , Yn are approximately iid with the normal 1 distribution N 0, n . This suggests a simple procedure that
Purdue - STAT - 520
464 675 703 887 1139 1077 1318 1260 1120 963 996 960 530 883 894 1045 1199 1287 1565 1577 1076 918 1008 1063 544 635 804 980 1018 1064 1404 1286 1104 999 996 1015 615 722 832 977 1270 1437 1520 1708 1151 934 1159 1209 699 830 996 1124 1458 1270 1753
Purdue - STAT - 520
101 82 66 35 31 7 20 92 154 125 85 68 38 23 10 24 83 132 131 118 90 67 60 47 41 21 16 6 4 7 14 34 45 43 48 42 28 10 8 2 0 1 5 12 14 35 46 41 30 24 16 7 4 2 8 17 36 5062 67 71 48 28 8 13 57 122 138 103 86 63 37 24 11 15 40 62 98 124 96 66 64 54 39 2
Purdue - STAT - 520
Statistics 520: Time Series and Applications Dr. LevinePurdue University Spring 2008IntroductionShumway and Stoffer: 1.1-1.4Jan, 2008 Page 1Statistics 520: Time Series and Applications Dr. LevinePurdue University Spring 2008Examples of t
Purdue - STAT - 520
Statistics 520: Time Series and Applications Dr. LevinePurdue University Spring 2008Stationarity and Correlation EstimationShumway and Stoffer: 1.5-1.6Jan, 2008 Page 1Statistics 520: Time Series and Applications Dr. LevinePurdue University
Purdue - STAT - 520
Exploratory Data Analysis of Time SeriesShumway and Stoffer: 2.31Determining the trend:regression approach Consider the model x t = t + twhere t is a stationary process while t is a stationary trend. A strong trend can obscure the behavior
Purdue - STAT - 520
Statistics 520: Time Series and Applications Dr. LevinePurdue University Spring 2008General ARMA(p,q) modelsShumway and Stoffer: 3.1-3.2Jan, 2008 Page 1Statistics 520: Time Series and Applications Dr. LevinePurdue University Spring 2008A
Purdue - STAT - 520
Purdue - STAT - 520
Purdue - STAT - 520
Purdue - STAT - 520
0.000431 -0.032049 -0.064579 0.037256 0.014549 0.055532 0.028476 0.027706 0.002458 -0.027810 0.027726 0.029064 0.001707 0.045159 0.006724 0.006786 0.057336 -0.020423 0.075360 0.025511 0.046540 -0.039414 0.069393 0.023042 -0.002745 -0.013542 0.089915
Purdue - STAT - 520
Additional: The best answer there is either AR(3), AR(5) or MA(3). If you try to take into account the higher order lags (say, above 10), that relatively high acf/pacf at those lags is usually the result of estimation errors and it is best to keep th
Purdue - STAT - 520
Purdue - STAT - 520
Purdue - STAT - 520
Purdue - STAT - 511
Instructor Office Phone E-mail Course webpage Office hours GraderProf. Michael Levine MATH 438 (765)496-7571 mlevins@stat.purdue.edu http:/www.stat.purdue.edu/~mlevins/Stat511/Stat511.htm Thursday: 2-3.30pm Friday: 2-3.30pm or by appointment Yang Z
Purdue - STAT - 511
TENTATIVE SCHEDULE Week Topic August 23rd- August 28th Chapter1 rd August 31st- September 3 Sections 2.1, 2.2 September 8th- September 10th Sections 2.3-2.5 th th September 13 - September 17 Sections 3.1-3.3 September 20th- September 24th Sections 3.
Purdue - STAT - 511
An exampleFor two-seaters on the highwayx_24 30 30 25.8 191. Mean as a non-resistant measure of the distribution center. It can be severely compromised by just one outlier; long tails also make it unrepresentative. A good example is the
Purdue - STAT - 520
STAT 520 TIME SERIES AND APPLICATIONS COURSE INFORMATIONCLASS MEETING TIME AND PLACE: TTh, 3.00-4.15pm, REC 307 Office hours: TTh, 2-3pm, HAAS 154 or by appointment http:/www.stat.purdue.edu/~mlevins/STAT520_07/STAT520_07.htm TEXTBOOK Introduction
Purdue - STAT - 520
-0.010381 -0.024476 -0.115591 0.089783 0.036932 0.068493 0.000000 0.000000 0.065104 0.032258 0.031250 0.030303 0.023041 0.081081 0.183333 0.078571 0.149007 -0.048991 0.085890 0.031073 0.019178 -0.008152 0.090411 0.218593 0.041667 0.028000 0.004864 -0
Purdue - STAT - 520
0.000431 -0.032049 -0.064579 0.037256 0.014549 0.055532 0.028476 0.027706 0.002458 -0.027810 0.027726 0.029064 0.001707 0.045159 0.006724 0.006786 0.057336 -0.020423 0.075360 0.025511 0.046540 -0.039414 0.069393 0.023042 -0.002745 -0.013542 0.089915
Purdue - STAT - 520
0.00632 0.00366 0.01202 0.00627 0.01761 0.00918 0.00820 -0.01170 -0.00587 0.00757 -0.00992 0.03989 0.02817 0.03682 0.02809 0.02073 0.02593 0.02202 0.00458 0.00969 -0.00241 0.00896 0.02054 0.01734 0.00939 -0.00465 -0.00810 -0.01398 -0.00399 0.01192 0.
Purdue - STAT - 520
3.7 3.4 3.4 3.1 3.0 3.2 3.1 3.1 3.3 3.5 3.5 3.1 3.2 3.1 2.9 2.9 3.0 3.0 3.2 3.4 3.1 3.0 2.8 2.7 2.9 2.6 2.6 2.7 2.5 2.5 2.6 2.7 2.9 3.1 3.5 4.5 4.9 5.2 5.7 5.9 5.9 5.6 5.8 6.0 6.1 5.7 5.3 5.0 4.9 4.7 4.6 4.7 4.3 4.2 4.0 4.2 4.1 4.340.0 41.0 43.0 42
Purdue - STAT - 520
vw &lt;- scan(file=&quot;U:/.www/Stat520_07/m-vw2697.txt&quot;) length(vw) acf(vw,lag=20) acf(log(vw+1),lag=20) ar3.t &lt;- ar(vw,method=&quot;ols&quot;,order.max=3) ar3.t$order [1] 3 ar3.t$ar ,1 [,1] [1,] 0.10406023 [2,] -0.01027165 [3,] -0.12041467 vw.subset &lt;- vw[1:858] ar
Purdue - STAT - 520
Statistics 520: Time Series and Applications Dr. LevinePurdue University Spring 2006Yule-Walker method For an AR(p) process Yt = 1 Yt1 + . . . + p Ytpthe system of Y-W equations is(k) = 1 (k 1) + + p (k p)where k= 1, . . . , p
Purdue - STAT - 520
Simple Forecasts Consider a signal plus noise model Yn = mn + Xn . The trend mn can beeasily estimated by, e.g., exponential smoothing. Then, if the trend is constant, the series is stationary and the best linear predictor of Yn+h is mn Remind
Purdue - STAT - 520
tt &lt;- read.table(file=&quot;U:/.www/Stat520_07/ustbill.dat&quot;,header=F) ttb &lt;- as.matrix(tt[,2:7]) ttb_m &lt;- t(ttb) ttbill&lt;- as.vector(ttb_m) plot.ts(ttbill) acf(ttbill) plot.ts(log(ttbill) acf(log(ttbill) dlntbill &lt;- diff(log(ttbill) plot.ts(dlntbill) acf(d
Purdue - STAT - 1
Problem 2.34 A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selection
Purdue - STAT - 511
Problem 2.34 A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selection