ENG 85-222
Graphing Data
Instructor: Dr. Lindsay Miller - Branovacki
Winter 2017
Data Displays
Univariate data analysis
Data list and array
Frequency distribution
Histogram
Frequency polygon
Relative frequency histogram
Cumulative relative frequenc
ENG 85-222
Summary Statistical Measures:
Shape
Relative Position
Instructor: Dr. Lindsay Miller - Branovacki
Winter 2017
Summary of Univariate Data
Quantitative
(numerical)
3 characteristics
Shape
Modality
(how many humps?)
Skewness
(symmetry, assymetry
ENG 85-222
Random Variables
Instructor: Dr. Lindsay Miller Branovacki
Winter 2017
Random Variables
Random variable is
Not a variable!
Not random!
Random variable is a function from sample
space to the real numbers
It assigns a real number to each outco
ENG 85-222
Introduction to Estimation
Confidence Intervals
Instructor: Dr. Lindsay Miller - Branovacki
What is estimation good for?
A lot of problems in engineering are
based on empirical observations
Observations deal with
measurements
Measurements are i
ENG 85-222
Conditional Probability
Counting Rules
Instructor: Dr. Lindsay Miller - Branovacki
Winter 2017
Dependent Events
When an outcome or occurrence of the first
event affects the outcome of the second event
in such a way that a probability is changed
ENG 85-222
Summary Statistical Measures:
Variability
Instructor: Dr. Lindsay Miller - Branovacki
Winter 2017
Summary of Univariate Data
Quantitative
(numerical)
3 characteristics
Shape
Modality
(how many humps?)
Skewness
(symmetry, assymetry)
Center
Spr
ENG 85-222
Probability Distributions in Engineering
Instructor: Dr. Lindsay Miller - Branovacki
Winter 2017
Cont. Probability Distribution Models
Continuous Probability
Distributions
Uniform
Normal
Exponential
Other
T-student
F-distribution
Chi-square
Wei
ENG 85-222
Summary Statistical Measures:
Location
Instructor: Dr. Lindsay Miller - Branovacki
Winter 2017
Some Statistics
Internet Statistics
http:/www.youtube.com/watch?v=7XyWTGepCHo
TED Talk Statistics
http:/www.youtube.com/watch?v=1Totz8aa2Gg
2 of 37
S
ENG 85-222
Normal Distribution
Instructors: Dr. Lindsay Miller Branovacki
Winter 2017
Importance of Normal Distribution
Describes many random processes or
continuous phenomena
Can be used to approximate discrete
probability distributions
Example: Binomial
4) Finding Roots
Last update: January 18
1
Introduction
We will consider the problem of finding the roots of a single equation. In general, to
find the roots of an equation we want to find the value or values of x that satisfy the
following equation:
For
ENG 85-222
Categorical Variables
Two Way Tables
Instructor: Dr. Lindsay Miller - Branovacki
Statistical Data
Qualitative data
involves attributes, such as occupation,
location or some other category
Quantitative data
represents the quantity or amount of
85-222 s1 W16 TREATMENT OF EXPERIMENTAL DATA
Exam Code
February 26, 2016
THIS IS A CLOSEDBOOK & -NOTES
EXAM
PROF. Z. PASEK
MID-TERM EXAM I
[]
11
First Name
SOLUTIONS
Last Name
Student ID
Honor Pledge: I have neither given nor received aid on this exam.
Ma
ENG 85-222
Binomial Distribution
Instructors: Dr. Lindsay Miller Branovacki
Winter 2017
Some Examples
Two nationwide surveys are planned to
estimate the proportion p of people who have
a favorable approval rating of the President.
The first survey will ra
ENG 85-222
Probability Rules & Representation
Instructor: Dr. Lindsay Miller - Branovacki
Winter 2017
Probability Calculations
Case 1: Outcomes Equally Likely
Formulas:
numberof outcomesin event
P (event)
#of possibleoutcomes
1
P (outcome)
#of possibleo
85-222 s1 W16 TREATMENT OF EXPERIMENTAL DATA
Exam Code
February 26, 2016
THIS IS A CLOSEDBOOK & -NOTES
EXAM
PROF. Z. PASEK
MID-TERM EXAM I
[]
22
First Name
SOLUTIONS
Last Name
Student ID
Honor Pledge: I have neither given nor received aid on this exam.
Ma
ENG 85-222
Expected Value & Variance
Instructor: Dr. Lindsay Miller Branovacki
Winter 2017
Expected Value and Variance
Its important to compute mean (expected value) and
variance of probability distribution. For example,
Recall from our discussion on ra
85-220 Numerical Analysis for
Engineering
2017 Winter
Faculty of Engineering
University of Windsor
1
1) Floating-Point Numbers
Last update: January 9
2
Floating-Point Numbers
Floating-point numbers are used to approximate the real number
system. There are
85-222 s1 W16 TREATMENT OF EXPERIMENTAL DATA
Exam Code
February 26, 2016
THIS IS A CLOSEDBOOK & -NOTES
EXAM
PROF. Z. PASEK
MID-TERM EXAM I
[]
33
First Name
SOLUTIONS
Last Name
Student ID
Honor Pledge: I have neither given nor received aid on this exam.
Ma
4) I/O in MATLAB
Last update: January 27
Input/Output
Input/output (aka I/O) is the communication between the computer
and something outside the computer, such as you the user or another
computer. You have already been using I/O when you use a keyboard
or
2) Computational Errors
Last update: January 11
1
Computational Errors
We can define two types of errors that can occur during computer
computations:
1) Round-off errors
2) Truncation errors
2
Round-Off Errors
Round-off errors come from two sources:
1) Th
3) Introduction to Numerical
Analysis
Last update: January 11
1
Introduction
To analyse a physical process we can:
Create a mathematical model
Run experiments
2
Introduction
Experiments have advantages:
Directly deal with the process under investigatio
Faculty of Engineering
University of Windsor
85-220 Numerical Analysis for Engineering
2016 Winter
Lab Assignment 1Solutions
Assigned:
Due:
Lab week of January 1822
In your lab
Note: (1) Make sure you sign the attendance sheet. You will not get credit for
Faculty of Engineering
University of Windsor
85-220 Numerical Analysis for Engineering
2016 Winter
Lab Assignment 3Solutions
Assigned:
Due:
Lab week of February 14
In your lab
Note: (1) Make sure you sign the attendance sheet. You will not get credit for
Faculty of Engineering
University of Windsor
85-220 Numerical Analysis for Engineering
2016 Winter
Lab Assignment 2Solutions
Assigned:
Due:
Lab week of January 2528
In your lab
Note: (1) Make sure you sign the attendance sheet. You will not get credit for
Chapter 4
Numerical Methods
4.1
Introduction
The majority of PDEs we use every day in applications cannot be solved by
analytic methods. In other words, we do not know how to nd an exact solution
for these PDEs. Therefore, it is important to be able to ap
Jim Lambers
MAT 460/560
Fall Semester 2009-10
Lecture 7 Notes
These notes correspond to Section 1.3 in the text.
Approximations in Numerical Analysis, contd
Convergence
Many algorithms in numerical analysis are iterative methods that produce a sequence cf
Programming Assignments
Introduction to Programming with MATLAB
Lesson 3
Unless otherwise indicated, you may assume that each function will be given the correct number of inputs
and that those inputs have the correct dimensions. For example, if the input