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School: Duke
Course: Intro To Mathematical Statistics
STA 250/MTH 342 Intro to Mathematical Statistics Lecture 11 If we have n i.i.d. N (0, 1) random variables U1 , U2 , . . . , Un , then the probability distribution of their sum 2 2 2 Z = U1 + U2 + + Un is called the 2 (or Chi-square) distribution with n de
School: Duke
Inference: MLE Sayan Mukherjee Lab assignment Three September 24, 2009 Sayan Mukherjee Inference: MLE Lab outline The lab will be due on the 2th of October. You will be expected to write a short: 1-2 page lab report. The 1-2 pages do not include plots or
School: Duke
Random variables: sampling and plotting Sayan Mukherjee and Artin Armagan Lab assignment Two September 10, 2009 Sayan Mukherjee and Artin Armagan Random variables: sampling and plotting Lab outline The lab will be due on the 18th of September. You will be
School: Duke
Course: Probability
Homework 3 MATH230 Due: October 1, 2012 1 Let Xi = the number on the ith roll, i = 1, 2, ., 10 10 E 10 Xi = i=1 E (Xi ) i=1 10 (1 + 2 + 3 + 4 + 5 + 6)/6 = i=1 = 10 3.5 = 35 2 This problem can also be solved using the tail probability formula for expectati
School: Duke
Course: Probability
Homework 4 MATH230 Due: October 12, 2012 Problem 1 a Xi [0, 1, 4, 9, 6, 5, 6, 9, 4, 1] E (Xn ) = E (Xi ) = (0 + 1 + 4 + 9 + 6 + 5 + 6 + 9 + 4 + 1)/10 = 4.5 b According to the Central Limit Theorem, as n approaches innite, Xn should be approximately normal
School: Duke
Course: Probability
Homework 2 MATH230 Due: September 14, 2012 Problem 1 Let B1 = rst ball, B2 = second ball P (B2 = white) = P (B1 = white, B2 = white) + P (B1 = black, B2 = white) = P (B2 = white|B1 = white)P (B1 = white) + P (B2 = white|B1 = black)P (B1 = black) = 7 13 4
School: Duke
Course: Probability & Measure Theory
School: Duke
Course: Probability & Measure Theory
School: Duke
Course: Probability & Measure Theory
N R Z R
School: Duke
Course: Probability & Measure Theory
School: Duke
Course: Probability & Measure Theory
School: Duke
Is The Relationship Really Linear? How About Residuals? Inuential Observations Example STA113 Regression Diagnostics Artin Armagan Department of Statistical Science November 18, 2009 Armagan Is The Relationship Really Linear? How About Residuals? Inuentia
School: Duke
Simple Linear Regression Analysis Multiple Linear Regression STA113: Probability and Statistics in Engineering Linear Regression Analysis - Chapters 12 and 13 in Devore Artin Armagan Department of Statistical Science November 18, 2009 Armagan Simple Linea
School: Duke
Course: Special Topics
%!PSAdobe2.0 %Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %Title: cluster_lecture.dvi %Pages: 22 %PageOrder: Ascend %Orientation: Landscape %BoundingBox: 0 0 612 792 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: d
School: Duke
Course: Statistics
STA 114/MTH 136 Intro to Mathematical Statistics Lecture 12 1 / 28 Central limit theorem allows to approximate the sampling distribution of an estimator if it can be written as the sum of i.i.d. random variables. This scenario occurs very often. For examp
School: Duke
Course: Statistics
STA 114/MTH 136 Intro to Mathetical Statistics Lecture 3 1 / 43 Last class Bayes Theorem and the ideal approach to inference. Example: A political poll (a binomial experiment). 2 / 43 Political poll example revisited An organization randomly selected 100
School: Duke
Course: Statistics
STA 114: Statistics Notes 17. Hypotheses testing Hypotheses about model parameters A new soporic drug is tried on n = 10 patients with sleep disorder, and the average increase in sleep hours is found to be 2.33 hours (with standard deviation 2 hours). Is
School: Duke
Course: Probability
Homework 3 MATH230 Due: October 1, 2012 1 Let Xi = the number on the ith roll, i = 1, 2, ., 10 10 E 10 Xi = i=1 E (Xi ) i=1 10 (1 + 2 + 3 + 4 + 5 + 6)/6 = i=1 = 10 3.5 = 35 2 This problem can also be solved using the tail probability formula for expectati
School: Duke
Course: Probability
Homework 4 MATH230 Due: October 12, 2012 Problem 1 a Xi [0, 1, 4, 9, 6, 5, 6, 9, 4, 1] E (Xn ) = E (Xi ) = (0 + 1 + 4 + 9 + 6 + 5 + 6 + 9 + 4 + 1)/10 = 4.5 b According to the Central Limit Theorem, as n approaches innite, Xn should be approximately normal
School: Duke
Course: Probability
Homework 2 MATH230 Due: September 14, 2012 Problem 1 Let B1 = rst ball, B2 = second ball P (B2 = white) = P (B1 = white, B2 = white) + P (B1 = black, B2 = white) = P (B2 = white|B1 = white)P (B1 = white) + P (B2 = white|B1 = black)P (B1 = black) = 7 13 4
School: Duke
Course: Probability
Homework 1 MATH230 Due: September 10, 2012 Part A P (rst ticket drawn is 1 and the second ticket drawn is 2) = P (rst ticket drawn is 1)P (second ticket drawn is 2) = 1 n = 1 n 1 n2 Part B Many students interpreted this question to mean that the second dr
School: Duke
Lab Assignment #6 STA 113 November 18, 2009 This is a real data set which was used in Leo Breiman and Jerome H. Friedman (1985), Estimating optimal transformations for multiple regression and correlation, JASA, 80, pp. 580-598. The problem is to predict t
School: Duke
Condence and credible intervals Artin Armagan Lab assignment #5 October 20, 2009 Artin Armagan Condence and credible intervals Lab outline The lab will be due on October 30th. You will be expected to write a short: 1-2 page lab report and also turn in cod
School: Duke
Inference: MLE and Bayesian Sayan Mukherjee Lab assignment Four October 1, 2009 Sayan Mukherjee Inference: MLE and Bayesian Lab outline The lab will be due on the 9th of October. You will be expected to write a short: 1-2 page lab report. The 1-2 pages do
School: Duke
Inference: MLE Sayan Mukherjee Lab assignment Three September 24, 2009 Sayan Mukherjee Inference: MLE Lab outline The lab will be due on the 2th of October. You will be expected to write a short: 1-2 page lab report. The 1-2 pages do not include plots or
School: Duke
Random variables: sampling and plotting Sayan Mukherjee and Artin Armagan Lab assignment Two September 10, 2009 Sayan Mukherjee and Artin Armagan Random variables: sampling and plotting Lab outline The lab will be due on the 18th of September. You will be
School: Duke
STA113 - Probability and Statistics in Engineering, Fall09 Instructors: Sayan Mukherjee and Artin Armagan e-mail: sayan@stat.duke.edu, artin@stat.duke.edu Oce: Old Chem 112, Old Chem 217 Oce hours: TBA Textbook: Jay L. Devore, Probability and Statistics f
School: Duke
Course: Intro Biostatistics
Syllabus STA102, Stangl, Spring 2005 Time and Location: Class M/W 1:15, Social Sciences 136 Instructor: Dalene Stangl Office: 212 Old Chemistry, dalene@stat.duke.edu, 684-4263 Texts: Fundamentals of Biostatistics (latest edition) by Rosner JMP IN S
School: Duke
Course: Data Analy Stat Infer
Data Analysis and Statistical Inference STA 101 Sec 2 Instructor: SYLLABUS AND COURSE POLICIES Fall, 2004 Teaching Assistants: TA Location: Course Web Page: Lectures: Computer Labs: Text: Woncheol Jang Old Chem 223B wjang@stat.duke.edu (919) 684-