STAT 231 ON-LINE QUIZ 2 SPRING 2010 Due: Monday May 16 12:00 noon Instructions: 1. Complete these questions first. 2. Enter your answers in Quiz 2 available in the Contents folder of the course web page on UW-ACE. You have one hour to complete the quiz on
Test 3 Questions 1. If Y is an exponential random variable with pdf f ( y ) = expcfw_ y / 3 / 3, y > 0 , then find a number t (to three decimals) so that P(Y > t ) = 0.05 .
2. Suppose Y1 ,., Y100 are independent exponential random variables with mean = 2
Quiz 4 Questions (Terminology review) To assess a measurement system used to inspect a critical dimension of an engine component, the system measures a verified standard of 3.0025 cm five times with results 3.002, 3.004, 3.003, 3.002, 3.0003. 1. Each act
STAT 231 Spring 2010 On-line Test 1 Solutions Read the following story and fill in the blanks with the best choice of PPDAC terminology spelling matters to Angel! Doctors want to investigate the value of taking vitamin D (2000 international units per day)
Maximum Likelihood Estimation
Week 3
Goals:
Review continuous probability models
More maximum likelihood estimation
Example 7
A study is conducted to look at the quality of bottled water sold in
Ontario. The goal is estimate the average number of bacteria
STAT 231, Statistics
Winter 2014
Course Outline
The Course Information Page
learn.uwaterloo.ca
You are expected to regularly read your email and visit the course website on D2L for announcements.
Instructors
Sec Instructor
001 Ilham Akhundov
002 Cyntha St
APPENDIX A. ANSWERS TO
ASSORTED PROBLEMS
Chapter 1
1.1. (a) average and median a + by ; a + bm respectively. (b) No relation in general but if
^
P
P
2 : (c) As a rule
all yi 0; then median(vi ) = m
^
(yi m) 6= 0 but (yi y ) = 0:
^
y +y
(d) a(y0 ) = nn+10
STAT 231 Tutorial Test 1: Week of January 20-24 in your
scheduled tutorial time. You may write ONLY in your
assigned tutorial time!
PINK TIE CALCULATORS ONLY. Bring your Watcard.
Check D2L for information about seating arrangements.
Tutorial Test 1 covers
A Brief Tutorial on R
B y: Krista Dow
R is available to download for free at:
http:/cran.r-project.org/
For more information and help with R see:
http:/www.stats.uwaterloo.ca/stats_navigation/statsoftware/R/
THE BASICS
Function/Ex.
Description
Information
sex length
F 93
F 97
F 92
F 101.6
F 93
F 84.5
F 102.5
F 97.8
F 91
F 98
F 93.5
F 91.7
F 90.2
F 91.5
F 80
F 86.4
F 91.4
F 83.5
F 88
F 71
F 81.3
F 88.5
F 86.5
F 90
F 84
F 89.5
F 84
F 85
F 87
F 88
F 86.5
F 96
F 87
F 93.5
F 93.5
F 90
F 85
F 97
F 86
F 73.7
M 97
Stat 231 Tutorial
Week 2 Solutions
1. Consider the following summary statistics taken from a random sample of n = 16
observations,
n
n
2
yi = 1163.56
yi = 106.27,
i=1
i=1
(a) Find the sample mean and sample standard deviation for this data
(b) If we colle
Stat 231 Tutorial
Week 2 Questions
1. Consider the following summary statistics taken from a random sample of n = 16
observations,
16
n
2
yi = 1163.56
yi = 106.27,
i=1
i=1
(a) Find the sample mean and sample standard deviation for this data
(b) If we coll
Statistical
Models,
Likelihood
function
Statistical Models, Likelihood function
Week 2
Statistical
Models,
Likelihood
function
Goals:
Review of important Stat230 topics
Connect probability models to the statistic process
Introduce the likelihood function
Introduction Basic Syntax R Studio R Commander Having Some "Fun" with R
R Tutorial - For Beginners
Statistics and Actuarial Science
FALL 2012
Statistics and Actuarial Science
1/ 47
Introduction Basic Syntax R Studio R Commander Having Some "Fun" with R
Ou
Your next test will be held on Tuesday, July 8 from 4:45
to 6:15 and will cover material to the end of section 5.3
(Material from Section 5.4 is NOT covered on this
test)
Please pay special attention to the suggested questions
posted on LEARN
You should
Last question was difficult
You cannot use the derivative approach to find the
mle
You needed to check boundaries afterward
Then, you needed to think about the distribution
itself, the likelihood function, and the data given
The likelihood function is MA
We have seen that confidence intervals for a parameter
tend to get narrower as the sample size n increases
When designing a study, we need to decide how large a
sample to collect based on:
i) how narrow we would like our confidence interval to
be
ii) how
We discussed the idea of point estimates and
point estimators. Hopefully things are clear now.
If not, please review this material again its
important!
An estimate will provide us with a single value, or
point
To indicate the uncertainty in an estimate w
Proposition
If L() is based on Y = (Y1, Y2, , Yn), a random
sample of size n, and if is the true value of the
scalar parameter, then, the distribution of the
likelihood ratio statistic converges to a 2(1)
distribution as n
What this means is that can be
~
We refer to as the (point) estimator
corresponding to the (point) estimate,
Notation: In this course, we will use to denote
~
an estimate (numerical value) and we will use to
denote the corresponding estimator (random
variable)
This is not notation ad
Stat 231 Case Study
Problem Set 1
The following questions deal with two case studies. A description of the studies (CaseStudy.pdf) and
the corresponding datasets (CaseStudy1.txt and CaseStudy2.txt) are available on the Learn website.
Case Study 1 - Prescr
Stat 231 Case Study
Description
Here we describe two case studies which will be analyzed throughout the course. The data for these
studies are not the actual values, but rather simulated data based on the summaries given in the corresponding articles. Ass