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### 324.12.02

Course: STAT 324, Fall 2008
School: Wisconsin
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Wisconsin - STAT - 324
Wisconsin - STAT - 324
Wisconsin - STAT - 324
Wisconsin - STAT - 324
Wisconsin - STAT - 324
Wisconsin - STAT - 311
Stat 311-Lecture 02, CombinatoricsSept 13, 2005 1. Given n distinguishable objects x1 , , xn , permutation is a rearrangement of the n objects. There are n! different rearrangements. Combination is a way to choose k objects out of the n distinct
Wisconsin - STAT - 311
Stat 311-Lecture 05, Random VariablesSept 20, 2005 1. Given a sample space S, a random variable X is a function that that maps an element in S to a real number, i.e. X : S R. A random variable is discrete if the number of elements in a sample spac
Wisconsin - STAT - 311
Stat 311-Lecture 06, ExpectationSept 22, 2005 1. The expected value of a discrete random variable X is dened as EX = xS xp(x). 2. Problem. A man with n keys wants to open his door and tries the keys at random. Exactly one key will open the door. Fi
Wisconsin - STAT - 311
Wisconsin - STAT - 311
Stat 311-Lecture 09 Continuous Random VariablesOct 6, 2005 1. The cumulative distribution of X is defined as F (x) = P (X x). F (-) = 0, F () = 1. 2. Problem. For X Binomial(n, p),iF (x) =y=0n y p (1 - p)n-y y accept=find(rsquare &lt;1); &gt; acc
Wisconsin - STAT - 311
Stat 311-Lecture 10 Normal DistributionOct 20, 2005 1. The expected value of a continuous random variable X with pdf f (x) isEX =- xf (x) dx.Eh(X) =-h(x)f (x) dx.2. The cumulative distribution function F of a continuous random variable
Wisconsin - STAT - 311
Stat 311-Lecture 13 Sum of random variablesNov 3, 2005 1. For random variables X and Y and their joint distribution f (x, y), the probability of P (X Y ) =xyf (x, y) dxdy.If X and Y are independent U nif (0, 1), the joint distribution is a un
Wisconsin - STAT - 311
Stat 311-Lecture 14 Conditional distributionsNov 10, 2005 1. The conditional probability mass function of Y given X = x is given by p(y|x) = p(x, y) . pX (x)5. Let X1 , X2 be i.i.d. Uniform(0,a) and let Y1 = min(X1 , X2 ), Y2 = max(X1 , X2 ). Fin
Wisconsin - STAT - 312
Stat312: Midterm Exam I.Instructor: Moo K. Chung mchung@stat.wisc.edu October 7, 2004Answer all questions clearly and circle your nal answer. Your answers should be correct up to the second decimal places. One page note and a calculator are allowed
Wisconsin - STAT - 312
Stat312: Sample Midterm IIMoo K. Chung September 30, 20041. Let X1 , , Xn be a random sample from Bernoulli distribution with parameter p. (a) What is E(S 2 /p2 )? S 2 is the sample variance. Explain your results (10 points). (b) Find an unbiase
Wisconsin - STAT - 312
Stat312: Final Exam SolutionsMoo K. Chung mchung@stat.wisc.edu December 17, 2004 N (0, 2 ). Derive1. We wish to fit data (x1 , y1 ), , (xn , yn ) with linear model Yj = 1 + xj + everything. (a) Find the maximum likelihood estimator for (10pt
Wisconsin - STAT - 312
Wisconsin - STAT - 312
Stat 312: Course OutlineMoo K. Chung mchung@stat.wisc.edu September 2, 20041. Lectures: TR 9:30-10:45 120 Ingraham 2. Class web: http:/www.stat.wisc.edu/mchung/ teaching/stat312/stat312.html Lecture notes and homeworks will be posted here. 3. Ofce
Wisconsin - STAT - 312
Stat 312: Lecture 01 R BasicsMoo K. Chung mchung@stat.wisc.edu September 2, 2004Histogram of a35Frequency&gt; a&lt;-bingePct &gt; mean(a) [1] 42.33571 &gt; var(a) [1] 205.8361 &gt; sd(a) [1] 14.34699 &gt; hist(a) To find out more about hist command, use &gt; help
Wisconsin - STAT - 312
Stat 312: Lecture 02 Point EstimationMoo K. Chung mchung@stat.wisc.edu September 2, 20041. If X and Y are independent, E(X + Y ) = EX + EY and V(X + Y ) = VX + VY . See pp. 244. 2. If a random sample Xi N (, 2 ), X 2 /n). N (, Proof. VX = E
Wisconsin - STAT - 312
Stat 312: Lecture 03 Minimum Variance Unbiased EstimatorMoo K. Chung mchung@stat.wisc.edu September 9, 2004 to the true parameter . X is MVUE for (we will not prove this statement). 4. Given a random sample X1 , , Xn , a linear estimator of par
Wisconsin - STAT - 312
Stat 312: Lecture 04 Moment MatchingMoo K. Chung mchung@stat.wisc.edu September 14, 20041. Given a random sample X1 , , Xn , a linear estimator of parameter is an estimator of formn4. Given random sample X1 , , Xn , the likelihood functio
Wisconsin - STAT - 312
Stat 312: Lecture 05 Maximum Likelihood EstimationMoo K. Chung mchung@stat.wisc.edu September 14, 2004^ 1. (Invariance Principle) If is the MLE's of ^ parameter then the MLE of h() is h() for some function h. Proof (partial). Consider likelihood
Wisconsin - STAT - 312
Stat 312: Lecture 06 Confidence IntervalsMoo K. Chung mchung@stat.wisc.edu September 21, 20041. A confidence interval (CI) is an interval used to estimate the likely size of a population parameter. A confidence level is a measure of the degree of r
Wisconsin - STAT - 312
Stat 312: Lecture 06 Quantile-quantile plotsMoo K. Chung mchung@stat.wisc.edu September 23, 2004F (q) = P (X q) = p. The textbook represent it in terms of percentile. Note that p-th quantile = 100 p-th percentile. So given p, q = F -1 (p). For X
Wisconsin - STAT - 312
Stat 312: Lecture 08 Large sample confidence intervalsMoo K. Chung mchung@stat.wisc.edu September 27, 20041. The sample size is inversely related to the width of confidence interval. Example 7.4. 2. Central Limit Theorem. Let X1 , , Xn be a ran
Wisconsin - STAT - 312
Stat 312: Lecture 09 Confidence intervals from normal populationMoo K. Chung mchung@stat.wisc.edu September 30, 2004Normal Q-Q Plot16 18 20 22 24 26 28 300.30 dt(x, 100) -4 -2 0 x 2 4 dt(x, 1) 0.4 0.0 -4 -2 0.2Sample Quantiles0.000.150 x
Wisconsin - STAT - 312
Stat 312: Lecture 2Moo K. Chung mchung@stat.wisc.edu January 23, 2003Definitions. 1. A statistic is a random variable from a random sample. If X 1 , , Xn is a random sample, a statistic is a function of them. 2. A point estimate of population p
Wisconsin - STAT - 312
Stat 312: Lecture 10 Confidence intervals for varianceMoo K. Chung mchung@stat.wisc.edu August 13, 20041. Suppose the fat content of a hotdog follows normal distribution. 10 measurements are given.dchisq(y, 1) 0.25 dchisq(y, 5) 0 20 y 400.000
Wisconsin - STAT - 312
Stat 312: Lecture 11 Hypothesis testingMoo K. Chung mchung@stat.wisc.edu Oct 20, 2004Concepts1. The null hypothesis H0 is a claim about the value of a population parameter. The alternate hypothesis H1 is a claim opposite to H0 . 2. A test of hypo
Wisconsin - STAT - 312
Stat 312: Lecture 15 P -valuesMoo K. Chung mchung@stat.wisc.edu November 2, 20041. The P -value is the smallest level of significance at which H0 would be rejected. Example 8.5, 8.15. Nicotine contents X1 , X32 of cigarettes follow N (, 0.22 ).
Wisconsin - STAT - 312
Stat 312: Lecture 17 Two sample t testMoo K. Chung mchung@stat.wisc.edu November 9, 20041. Let X1 , , Xn and Y1 , , Ym be two independent samples from normal distributions with the same population variance, i.e. Xi N (X , 2 ) and Yj N (Y
Wisconsin - STAT - 992
Stat 992: Lecture 40 Image Registration II.Moo K. Chung mchung@stat.wisc.edu December 5, 2003The total amount of displacement is u0 + u1 . Following this idea, we have iterative shifting algorithm un+1 (x) = Kn (g(x + u0 + u1 + un ) f (x) . Kn
Wisconsin - STAT - 992
Stat 992: Lecture 41 Image Analysis via Random Fields and Kernel Smoothing: OverviewMoo K. Chung mchung@stat.wisc.edu December 7, 2003Although it may be difcult to formulate all the problems in image analysis in terms of random elds and kernel smo
Wisconsin - STAT - 992
Topics mentioned briefly Topics covered Topics covered In detailSTAT 992: Streamlined Image Analysis FrameworkMoo K. Chung mchung@stat.wisc.edu 1. Image collection MRI, fMRI, PET, CT, EEG, MEG 2. Reading Image into computer Image formats ascii, bi
Wisconsin - STAT - 471
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Wisconsin - STAT - 471
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Wisconsin - STAT - 471
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Wisconsin - STAT - 471
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Wisconsin - STAT - 471
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Wisconsin - STAT - 471
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Wisconsin - STAT - 471
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Wisconsin - STAT - 471
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Wisconsin - STAT - 471
GNU OctaveA high-level interactive language for numerical computations Edition 3 for Octave version 2.0.13 February 1997John W. EatonPublished by Network Theory Limited. 15 Royal Park Clifton Bristol BS8 3AL United Kingdom Email: info@network-th
Wisconsin - STAT - 351
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Wisconsin - STAT - 351
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Wisconsin - STAT - 351
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Wisconsin - STAT - 351
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Wisconsin - STAT - 351
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Laurentian - BIOL - 3520
General Overview Preface There are two main aims of the lab section of this course. The first is to introduce you to Invertebrate and Protist biodiversity. At the outset, we must recognize that as far as invertebrate biodiversity goes, we live in a d
Laurentian - BIOL - 3520
Laurentian - BIOL - 3520
Laurentian - BIOL - 3520
Laurentian - BIOL - 3520
Clayton - PROJECT - 12850
Interoffice MemoDate: 3/29/2003 To: Cc: Edith Rowe Tina Rowe From:Ike Rowe RE: Ike's Auto Mechanic On Wheels WebsiteEdith please keep in mind that I might have to add or delete Web pages during the development process.IR/IR3/29/2003Confident
Clayton - PROJECT - 12850
I.A. B.Definition of the ClientClient /Ike Rowe The Designer - Edith RoweII.A.Goals of Web SiteThe goals of the web site are: - Focus on diagnosing and solving Customers Automotive problems -One-on-One customer relationship environment -Pro
Clayton - PROJECT - 12850
Page Layout and Design ModelHome PageMore About Ike's History Car Care Tips Services &amp; Repairs Questionnaire Customer Feedback MSN Auto Profile Yahoo! AutosIke's Auto Mechanic On WheelsImage 1 Image 2 Divider TextNavigation LinksImage 3Hor
Clayton - PROJECT - 12850
Graphics RequirementsThis website consist of GIF and JPEG Images. There is one photograph from The client. In addition to images, graphics such as lines and buttons will be added to enhance the overall appearance of the Website. The Images are as fo
Clayton - PROJECT - 12850
Graphics RequirementsThis website consist of GIF and JPEG Images. There is one photograph from The client. The designer will provide the remaining images. In addition to images, graphics such as lines and buttons will be added to enhance the overall
Clayton - PROJECT - 12850
Website Project User Task ListHome Page Company overview Access information, which also include the location, and the business telephone number about Ike's Auto Mechanic On Wheels organization Car Care Tips Services &amp; Repairs Questionnaire Customer
Clayton - CSU - 12850
This is the final draft received from my client Mr. Ike Rowe on 4/27/03- Original Message -From: Ike Rowe To: Edith Rowe (Web Designer) Sent: Sunday, April 27, 2003 7:16 PM Subject: Ike's Auto Mechanic On wheels Website - Final DraftDear Edith, I