Homework set 4  Due 02/22/13
Math 3200 Renato Feres
Preliminaries
Reading data into R. For this assignment, you will need to download the data les for the exercises in our statistics textbook. Go to the online course syllabus http:/www.math.wustl.edu/ fe
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lect 6. Review of Probability V
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
Feb. 1st, 2016
Outline
1
Expected Value, Variance, and Other Summary Measures
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lect 3. Review of Probability II
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
January 25, 2016
Outline
1
Basic Notions and Properties of Probability (Sect
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lect 5. Review of Probability IV
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
January 29, 2016
Outline
1
Random Variables and Their Distributions (Section
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lect 4. Review of Probability III
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
January 27, 2016
Outline
1
Conditional Probability (Section 2.2)
Definition
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lecture 7: Review of Probability VI
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
Feb. 3rd, 2016
Outline
1
Jointly Distributed Random Variables (Section 2.
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lecture 11: Review of Probability X
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
Feb. 12, 2016
Outline
1
Normal or Gaussian Distribution (Section 2.9)
Rev
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lecture 8: Review of Probability VII
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
Feb. 5th, 2016
Outline
1
Jointly Distributed Random Variables (Section 2
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lecture 9: Review of Probability VIII
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
Feb. 8th, 2016
Outline
1
Selected Discrete Distributions (Section 2.7)
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lecture 10: Review of Probability IX
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
Feb. 10, 2016
Outline
1
Selected Continuous Distributions (Section 2.8)
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lecture 12: Summarizing and Exploring Data I
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
Feb. 15, 2016
(Acknowledgment: some of these slides are taken fr
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Spring 2014
1. Using R: Ex 7.13 (use t.test function in R).
One Sample ttest
(a)
data: o
t = 3.4131, df = 19, pvalue = 0.002917
alternative hypothesis: true mean is not equal to 87
95 percent confidence interval:
87.15277 87.63723
sample estimates:
mean of x
87.395
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lect 2. Review of Probability I
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
January 22, 2016
Outline
1
Basic Notions of Probability (Section 2.1)
General
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2013
Math 3200
Lect 1. Brief Overview of Statistics and Probability
Jos E. FigueroaLpez1
1
Associate Professor
Department of Mathematics
http:/pages.wustl.edu/figueroa
Washington University in St. Louis
January 20th, 2016
Outline
1
Introduction to Statistics
Homework set 5  Solutions
Math 3200 Renato Feres
1. Illustrating the central limit theorem. Let X be a random variable having the uniform distribution over the
interval [1, 2]. Denote by X 1 , X 2 , X 3 , . . . a sequence of independent random variables
Homework set 7  Solutions
Math 3200 Renato Feres
Preliminaries
The Students t Test. A very common problem in statistics is to estimate the population mean of a probability
distribution given a sample, the subject of sections 7.1 and 7.2 of the statistics
Exam 1  Math 3200  Solutions
Spring 2013
1. Without actually expanding, nd the coefcient of x y 2 z 3 in the expansion of (2x y z )6 .
(A) 120
(B) 60
(C) 30
(D) 20
(E) 10
(F) 10
(G) 20
(H) 30
(I) 60
(J) 120
The monomial we want in the multinomial expans
Math 3200 Spring 2013  HW 0
Renato Feres  Wash. U.
This homework assignment wont be collected, but do it as soon as possible. Its purpose is to have the R program
up and running and getting a rst taste of how to use it for basic math.
1. Installation. C
Homework set 8  4/05/2013
Math 3200 Renato Feres
Problems
1. Problem 8.6, textbook, page 292. Production lines in a manufacturing plant are set to make steel ball bearings
with a diameter of 1 micron. Ten ball bearings were randomly selected from two pro
Homework set 9  Due 4/19/2013
Math 3200 Renato Feres
Preliminaries
The purpose of this homework assignment is to introduce some of the Rfunctions that can be used to perform the
kind of data analysis we studied in chapters 7, 8, and 9. Not all the tests
Homework set 10  Due 4/26/2013
Math 3200 Renato Feres
Preliminaries
The point of this assignment is to show how to do simple linear regression analysis in R. Not everything we describe
in these preliminaries is needed for the homework problems. Much of t
Homework set 7  3/29/2013
Math 3200 Renato Feres
Preliminaries
The Students t Test. A very common problem in statistics is to estimate the population mean of a probability
distribution given a sample, the subject of sections 7.1 and 7.2 of the statistics
Homework set 6  Due 03/22/13
Math 3200 Renato Feres
Preliminaries
Condence intervals. The meaning of the statement that the condence level is 95% lies in the frequentist interpretation of condence intervals (textbook, pages 204205): In a sequence of ind
Homework set 5  Due 03/01/13
Math 3200 Renato Feres
Preliminaries
The theory related to this assignment is in chapter 5, sections 14 of the statistics textbook.
Histograms and empirical densities. Let x be a vector containing observations of a random va
Homework set 10  Due 4/26/2013
Math 3200 Renato Feres
Preliminaries
The point of this assignment is to show how to do simple linear regression analysis in R. Not everything we describe
in these preliminaries is needed for the homework problems. Much of t
Homework set 3  Solutions
Math 3200 Renato Feres
1. Playing darts, I. In this experiment a person throws darts on a dartboard of radius 1. Each time the dart is
thrown, it is assumed to hit at a random point with coordinates (X , Y ) centered at the orig
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Spring 2014
Math 3200
Name_
ID_
Mathematics 3200
Midterm IV
April 13, 2015
Directions:
This is an optional midterm, which you may be used to replace your lowest midterm.
This exam consists of three parts. Part I has 5 points, Part II has 8 points, and Part III has 2
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Spring 2014
Math 3200 HW#1
January 22, 2015
Ex 3.1
(a)
i)
Because the study only passively records the interview data to estimate the proportion
with a gang afliation, this study is observational.
ii) this study is descriptive because the study estimates the proporti
Elementary and Intermediate Statistics with Data Analysis
MATH 3200

Fall 2015
MATH 3200
PROBABILITY AND STATISTICS
M3200FL153.1
In almost all problems, I have given the answers to four significant digits. If your answer is slightly different from one of mine,
consider that to be roundoff error and mark the closely matching one. If
Assignment 11
Changyi Li
10.4
(a)
>data1<read.delim("~/Downloads/Tamhane_Data/ASCII/Chapt10/Ex10_4.txt",
stringsAsFactors=FALSE)
> View(data1)
> plot(data1$LAST,data1$NEXT,xlab="last",ylab="next")
#The relationship appear to be approximately linear
(b)
>
Problem 10
Please see sample code for details.
(d):
(a)
(e):
The histograms above have similar shapes (approximately normally distributed). This is a
result of the Central Limit Theorem: If samples are taken i.i.d. from a distribution, then
when size n ,