14:06 Tuesday, March 28, 2017 1
d.a
The ANOVA Procedure
*Please note that R starts on Page 41
Research Questions:
The following are the objectives of this case study:
1. Determine whether or not the average biomarker scores differ among patients in differ
1/11/2016
Learning Objectives
Sample Space
Events
Counting Sample Points
Probability of an Event
Additive Rules
Conditional Probability, Independence, and
the Product Rule
Bayes Rule
1
Conditional Probability
Returning to the die tossing experiment for
1/15/2016
Random Variables and
Probability Distributions
Chapter 3
1
Learning Objectives
Concept of a Random Variable
Discrete Probability Distributions
Continuous Probability Distributions
Joint Probability Distributions
Marginal Distributions
Conditio
1/11/2016
Probability
Chapter 2
1
Learning Objectives
Sample Space
Events
Counting Sample Points
Probability of an Event
Additive Rules
Conditional Probability, Independence, and
the Product Rule
Bayes Rule
2
1
1/11/2016
Definitions
Probability refers t
Welcome to ENGR 20: Probability
and Statistics for Engineers I
1
Introduction to Statistics and Data
Analysis
Chapter 1
2
1
Learning Objectives
Statistical Inference, Samples, Populations and
the Role of Probability
Sampling Procedures; Collection of Da
1/11/2016
Probability
Chapter 2
1
Learning Objectives
Sample Space
Events
Counting Sample Points
Permutations
Combinations
Probability of an Event
Additive Rules
Conditional Probability, Independence, and
the Product Rule
Bayes Rule
2
1
1/11/2016
Mathematical Expectation
Chapter 4
1
Learning Objectives
Mean of a Random Variable
Variance of a Random Variable
Variance and Covariance of Random Variables
Means and Variances of Linear Combinations
of Random Variables
2
1
The Expected Value and Variance
1/11/2016
Probability
Chapter 2
1
Learning Objectives
Sample Space
Events
Counting Sample Points
Permutations
Combinations
Probability of an Event
Additive Rules
Conditional Probability, Independence, and
the Product Rule
Bayes Rule
2
1
1/11/2016
Statistics 1040
Summer 2009
Exam III
NAME_
Point score_ Curved Score_
Each question is worth 10 points. There are 12 questions, so a total of 120 points is possible.
No credit will be given unless your answer in clearly explained and/or all calculations s
Statistics 1040
Summer 2009
Exam III
1. For the following basic probability questions. Give the RULE used in the appropriate blank (BEFORE the
question), for each of the following situations, using one of the following letters:
a. Simple multiplication ru
population size 100,000, 20% well-educated; sample size 1,600 THE CHANCE ERROR IN A SAMPLE PERCENTAGE A certain town has a population of 100,000 people age 18 and over. 20% of these people are well-educated, that is, have college degrees. A simple random
Mean and Standard Deviation of Binomial Distribution
Binomial distribution comes from a series of Bernoulli trials (an experiment with two outcomes, "suceess" and
"failure", where we translate "success" as the number 1, and "failure" as zero).
The basic q
REGRESSION ASSIGNMENT
Statistics 1040 Dr. McGahagan
Spring 2015
The Penn World Tables (PWT) provides us with the material for this assignment.
We will try to find the best equations to explain the variables:
gdp.pc (Gross Domestic Product per Capita)
grat
Hypothesis testing - an introduction to the language.
We might be encouraged when a political poll shows the opposition candidate trailing by two percent,
but others will say that this is such a small difference that it may be due to chance error. To conv
Linear Regression - Notes on Chapter 7 of text
Please be sure to read the Learning Objectives for this chapter at openintro.org,
and looking over the lab on baseball would be helpful as well.
Some notes on the terminology I will expect you to know (multip
The following article appeared in the Lafayette Journal &
Courier on November 30, 1974:
Praying to soybeans aids in higher yields
By George Cornell
With county ocials measuring the results, experimenters
on an Ohio farm say they found that portions of a
Confidence Intervals, Hypothesis Testing and P-values
Dr. McGahagan Statistics
All the above involve asking the basic question: how sure are we about what we know?
The basic fact of life that inferential statistics has to deal with is that we seldom know
Statistics 1040
Dr. McGahagan
Final Exam
Summer 2008
Name_
Score_ Letter grade_
1. A fair die is rolled 7 times. What is the probability of:
_a. Getting ALL aces (one-spots) in 7 rolls of the die.
(1/6) to the 7th power = .00000357 or .000357 percent or 3
Statistics 1040
Dr. McGahagan
Spring 2015
Installing and Updating R
First, obtain a copy of the R program from the Comprehensive R Archive Network:
- search for CRAN R in your web browser
- choose a mirror for faster downloading (I suggest cran.case.edu u
Statistics 1040
Review Questions - Chapter 13
What are the Chances?
Problem 1. True/False.
a. Nothing can have probability 1000 percent - probability values are restricted to zero to one, or to zero
percent to 100 percent. Note that 1.00 = 100 percent, ju
Reviewing for Exam 3
Important concepts, formulas, and problems to review
FPP = Freedman, Pisani, and Purves, Statistics, 3rd edition.
Chapters 13-18 will be covered on the exam. Highlighted problem sets are especially important.
Answers to in-chapter pro
LISTING THE WAYS
A pair of dice are to be thrown. What is the chance of
getting a total of 7 spots?
There are
1q
2q
3q
4q
5q
6q
1 w, 5 e , 2 w,
possible ways for 2 dice to fall:
1w
2w
3w
4w
5w
6w
1e
2e
3e
4e
5e
6e
1r
2r
3r
4r
5r
6r
1t
2t
3t
4t
5t
6t
the
In poker (ve-card draw), the chance of being dealt a full
house (one pair and three of a kind) is about 0.14%.
INTRODUCTION
The chance of something happening gives the percentage
of time it is expected to happen, when the basic process is
done over and
Statistics 1040
Dr. McGahagan
Recommended problems from Open Intro Statistics, Chapter 2 - Probability
(Questions on pp. 107-113)
Note: answers to odd-numbered questions are on pages 390-391
The highlighted problems are especially important.
Defining prob
Bayes problems
Dr. McGahagan - Stat 1040
Problem 1. What is the relation between AND, OR and IF?
Specifically, note that in rolling 2 dice (Green and Red, with the Red die being rolled first)
Consider the two events: i. The two dice show a total of 10
ii.
Bayes' rule and revision of probabilities
Consider the probabilities of:
1. Drawing a king from a deck of cards (prior to any other information; hence the name of prior
probability). P(K) = 4/52
2. Drawing a king from a deck of cards (after a friend peeks
Statistics 1040 Dr. McGahagan
More Bayesian problems.
Problem 1. Election with two candidates, Rendell and Swann (candidates for Pennsylvania governor in
2000). Sixty percent of the people who live in the east support Rendell, 55 per cent of people who li
Dr. McGahagan - Statistics - Spring 2013-14
Assignment 1. Simulating some data and using R graphics.
PREPARATION
Not too much of this will work if you do not:
1. Have R on your computer or use it on a lab computer.
Note that the Macs have R installed, but
Data and Histograms.
Prof. McGahagan Stat 1040
We are told that the distribution of income (in thousands of dollars) by population is:
Income Range
Percent of population
[ 0 - 30 ]
25 %
(30 - 50 ]
50 %
(50 500 ]
25 %
Note that the parentheses are not squa