Springer Texts
in Statistics
Series Editors:
G. Casella
S. Fienberg
I. Olkin
For further volumes:
http:/www.springer.com/series/417
Modern
Mathematical
Statistics with
Applications
Second Edition
Jay L. Devore
California Polytechnic State University
Kenne
ST259 Probability I
Lecture Plan
Sept 8, 2016
Announcements
1. Introduction
2. Office Hours
3. Labs start next week
Readings
1. D&B Chapter 1 (review)
a. Be sure you are comfortable with measures of location (mean and median) and
measures of variability.
ST259 Probability I, Fall 2016
ST259 Recommended Homework
Please note the following:
This list represents the minimum number of practice problems that should be attempted when
studying for this course. It is strongly recommended that students try other p
ST259 Probability I, Fall 2016
Lecture Plan
Oct 4, 2016
Announcements
1. Completed excel spreadsheet for Example on Slide 7 has been posted
a. The pmf charts look fantastic
2. Excel spreadsheet for Example on Slide 10 has been posted
3. Homework exercise
ST259 Probability I, Fall 2016
Lecture Plan
Oct 20, 2016
Announcements
1. Be sure to get the Excel spreadsheets posted under Lecture Supplements on MyLS
2. Homework exercises and solutions for Chapter 3 (sections 3.4-3.7) have been posted
3. Midterm Exam
ST259 Probability I, Fall 2016
Midterm Exam Material
The midterm exam will cover everything up to Section 3.4 (Moments and Moment Generating
Functions) in the textbook.
Mark Reesor
ST259 Probability I, Fall 2016
Lecture Plan
Sept 15, 2016
Announcements
1. Tuesday Sept 20, have Dr. Sunny Wang as a guest lecturer
2. Why is P(S)=1?
a. Think of this as analogous to the Celsius temperature system
i. Why is Zero degrees Celsius the temper
ST259 Probability I, Fall 2016
Lecture Plan
Sept 13, 2016
Announcements
1. Labs start this week
2. If you have a computer, you should download and install R and R studio
a. https:/www.r-project.org/
i. To download R
b. https:/www.rstudio.com/
i. To downlo
ST259 Probability I, Fall 2016
ST259 Recommended Homework
Please note the following:
This list represents the minimum number of practice problems that should be attempted when
studying for this course. It is strongly recommended that students try other p
ST259 Probability I, Fall 2016
ST259 Recommended Homework
Please note the following:
This list represents the minimum number of practice problems that should be attempted when
studying for this course. It is strongly recommended that students try other p
ST 259 Lab Notes
Text References: 2.1, 2.2, 2.4, 2.5
Sample Spaces and Events (2.1)
Definitions:
Experiment - An action or process where the result is uncertain.
Sample Space - The set of all outcomes of an experiment.
Event - Any collection of outcomes f
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2: HS; 6:95 2: 3251
ST 259 Lab Notes
Text References: 2.1, 2.2
Sample Spaces and Events (2.1)
Definitions:
Experiment - An action or process where the result is uncertain.
Sample Space - The set of all outcomes of an experiment.
Event - Any collection of outcomes from the sa
ST 259 Lab Notes
Discrete Probability Distributions (3.5 - 3.7)
Random Variable Definitions:
Uniform Each value of X is equally likely to occur.
Bernoulli X represents a success (with probability p) or failure of a single Bernoulli trial.
Binomial X repre
ST 259 Lab Notes
Text References: 3.1 - 3.4
Random Variables (3.1)
Random Variable - A function that assigns exactly one number to each outcome in a sample space S. The
space of a random variable X is cfw_x : X(s) = x R, s S
Discrete Random Variable - A r
ST 259 Lab Notes
Text References: 4.2 - 4.4
Expected Values and Moment Generating Functions (4.2)
Let X be a continuous random variable with p.d.f f (x) and c.d.f F (x).
Definitions:
1. The mean or expected value of X is
Z
x f (x) dx
X = E(X) =
2. If h(X)
ST 259 Lab Notes
Probability Density Functions and Cumulative Distribution Functions (4.1)
Recall: A random variable X is continuous if there exists a function f : R [0, ) such that:
Zb
P (a X b) = f (x) dx for all a, b R
a
Definitions:
1. The function, f
ST259 Probability I, Fall 2016
Lecture Plan
Oct 6, 2016
Announcements
1. Have a great reading week!
2. Be sure to get the Excel spreadsheets posted under Lecture Supplements on MyLS
Readings
1. D&B Chapter 3.3, 3.4
Learning Objectives
At the end of this c
ST259 Probability I
Discrete Random Variables and Probability
Distributions
c
Mark
Reesor
mreesor@wlu.ca
Tower
Discrete RVs
Random Variables
Definition: Random Variable
For a given sample space S of some experiment, a random
variable is any rule that asso
c
ST 259 Midterm Test Answers Mark
Reesor
[3 marks]
Page 1 of 4
1. State the axioms of probability.
Solution: See lecture notes or textbook.
[3 marks]
2. Suppose that A and B are events such that P (A) = 0.5 and P (B) = 0.6. Is it possible that
A and B ar
CHAPTER FOURTEEN
Alternative
Approaches
to Inference
Introduction
In this final chapter we consider some inferential methods that are different in
important ways from those considered earlier. Recall that many of the confidence
intervals and test procedur
CHAPTER THREE
Discrete Random
Variables and
Probability
Distributions
Introduction
Whether an experiment yields qualitative or quantitative outcomes, methods of
statistical analysis require that we focus on certain numerical aspects of the data
(such as a
CHAPTER FOUR
Continuous
Random Variables
and Probability
Distributions
Introduction
As mentioned at the beginning of Chapter 3, the two important types of random
variables are discrete and continuous. In this chapter, we study the second general
type of r
ST259 Probability I, Fall 2016
CHAPTER 3
Section 3.1:
1: see text
2:
X = 1 if a randomly selected book is non-fiction and X = 0 otherwise
X = 1 if a randomly selected executive is a female and X = 0 otherwise
X = 1 if a randomly selected driver has automo
ST259 Probability I, Fall 2016
Lecture Supplement for September 27 Lecture
September 28, 2016
Solution to Example 1 on Lecture Slide 37:
At first glance our intuition might say, the more games against team B, the better chance of winning two
games in a ro
Lecture Supplement for Lecture on Sept 13
c
Mark
Reesor
September 15 2016
1
Proving Some Properties of Proabability using the Axioms of Probability
1. Use the axioms of probability to show that P (A \ B) = P (A) P (A B)
Solution: For any events A and B it
ST259 Probability I, Fall 2016
Note: Answers to only the even numbered questions are provided. For answers to the odd-numbered
questions appear please consult the back of the textbook, pages 814 834.
CHAPTER 2
Section 2.1:
1) Consider the following Venn D
ST259 Probability I
Discrete Random Variables and Probability
Distributions
c
Mark
Reesor
mreesor@wlu.ca
Tower
Discrete RVs
Random Variables
Definition: Random Variable
For a given sample space S of some experiment, a random
variable is any rule that asso
ST259 Probability I
Introduction to Probability
c
Mark
Reesor
mreesor@wlu.ca
Tower
Probability
Random Experiment
Definition: Random Experiment
A random experiment is any phenomenon that can in principle
be repeated indefinitely under identical conditions.
ST259 Probability I, Fall 2016
Lecture Plan
Sept 27, 2016
Announcements
1. None
Readings
1. D&B Chapter 2.4, 2.5
2. D&B Chapter 3.1 (if have time)
Learning Objectives
At the end of this class, students should be able to
1. Use and understand Bayes Rule
2.
ST 259 Lab 2 Notes
Text References: 2.3 - 2.5
Counting Techniques (2.3)
Multiplication Principle - If sets A1 , A2 , ., Ak have n1 , n2 , ., nk elements respectively, then there are
n1 n2 . nk ways of selecting one element from A1 , one element from A2 ,