Summary of 2.1
Distribution (Parameters) | Prob. Space
Bernoulli cfw_p p: prob of success # of successes in a
trial
Binomial cfw_n.p) n: xed # of trials # of successes in n
p: prob of success iid Bernoulli trials
Geometric (p) p: prob of success # of tria
MAT224H1F: Linear Algebra II
Problem Set #6
Solutions to Tutorial Problems
1. Let T : P2 (R) R3 be defined by
f(0)
T (f(x) = f(1) .
f(2)
Let = cfw_1, x, x2 , and be the standard basis of R3 .
(a) Find [T ] .
(b) Show thatT
is an isomorphism.
a
(c) Find T
Midterm Review
What to do:
Read lectures 1-6
Do the assigned exercises from the textbook
Go over the quiz questions
Use sample tests to practice
Use extra TAs' office hours
1. Given that A and B are independent with ( ) = 0.8 and ( ) = 0.3, find
P(A)
MAT224H1F: Linear Algebra II
Final Exam Review Sheet
G ENERAL C OMMENTS
This document is designed to help students prepare for the final exam in MAT224F.
However, it is absolutely not intended to summarize or be a substitute for the lecture
notes and prob
MAT224H1F: Linear Algebra II
Problem Set #7
Solutions to Tutorial Problems
Tutorial Problems
1. Let = cfw_1, x, x2 , x3 and = cfw_1, x1, (x1)2 , (x1)3 . These are both bases for P3 (R).
Find the change of basis matrices [I] and [I] . (Here I is the ident
MAT224H1F: Linear Algebra II
Problem Set #4
Solutions to Tutorial Problems
1. (a) Suppose V is an n-dimensional vector space, and is a basis of V. Let Id : V V
be the identity transformation, i.e. the transformation defined by Id(v) = v. Show that
[Id] is
University of Toronto
Faculty of Arts & Science
MAT224H1F: Linear Algebra II
Quiz #1
LEC 5101
Instructor: P. Crooks
SOLUTIONS
1
1. In each of the following cases, determine whether U is a subspace of V . Justify your conclusions. [10 marks]
(a) V = P2 (R)
Example 1
The interest rate is of 5% per
annum simple. Calculate the
amount of money which must be
invested on January 1, 2004 to
produce $1,500 on January 1,
2014.
Example 2
Mr. Chan deposits $1,000 on
January 1, 2007 at a rate of i
effective. Mrs. Smith
Workers Benefit Fund (WBF) Assessment
Workers Benefit Fund (WBF) Assessment
Table of Contents
Background 2
Subjectivity 3
Assessment Rate 5
Determining Hours Worked 6
Calculating the Assessment 8
Reporting 10
Amending Forms 13
Credit Transfer or Refund 14
Chapter 5
Summarizing Bivariate
Data
Weight
Suppose we found the age and weight
for each person in a sample of 10
adults. Is there any relationship There
between the age and weight of does not
these
appear to
adults?
Do you think there is a be a
relations
Chapter 9
Confidence Intervals
Suppose we wanted to estimate the
proportion of blue candies in a VERY
large bowl.
How might we go about estimating this
proportion?
We could take a a
We would have
sample of candies
sample proportion
and a statisticthe
or c
Chapter 12
The Analysis of
Categorical Data and
Goodness of Fit Tests
Suppose we wanted to determine if the
proportions for the different colors in a
large bag of M&M candies matches the
proportions that the company claims is
in their candies.
k is used t
Chapter 4
Numerical Methods
for Describing Data
Population characteristic
Suppose we want to know the MEAN
-length of all the fish in Lake Lewisville .
Fixed value about a population
.
Is this a value that is known?
Typical unknown
Can we find it out?
At
Chapter 2
Collecting Data Sensibly
Note: Correct usage of the vocabulary in this
chapter is VERY important!
Consider the imply that spanking is the
These headlines following headlines
CAUSE of the observed difference in 25,
which occurred on SeptemberIQ.
Chapter 6
Probability
Suppose two six-sided die is rolled and
they both land on sixes.
Or a coin is flipped and it lands on
heads.
Or record the color of the next 20 cars
to pass an intersection.
These would be examples of chance
experiments.
Chance exper
Chapter 13
Simple Linear
Regression and
Correlation: Inferential
Methods
Suppose we were to investigate the
relationship between y = the first-year
college grade point average and x = high
school grade point average.
The first-year college grade
Is point
Chapter 8
Sampling Variability and
Sampling Distributions
Suppose we are interested in finding the
true mean () fat content of quarter-pound
hamburgers marketed by a national fast
food chain. To learn something about , we
To answer these questions, we wil
Chapter 14
Multiple Regression
Analysis
What is the general purpose of
regression?
To model the relationship between the
Multiple regression can be used to fit
dependent variable y (response) and one or
models to data with two or more
more independent va
Chapter 1
The Role of Statistics
and the Data
Analysis Process
What is statistics?
the science of collecting,
analyzing, and drawing
conclusions from data
Why should one study
statistics? Can dogs help
patients with
1. To be informedheart failure by
.
a)
Chapter 7
Random Variables and
Probability Distributions
Random Variable AA grocery store manager might be
numerical variable whose value
interested in the number of broken
depends on the outcome of of chance
a
eggs in each carton (dozen
experiment eggs).
Chapter 3
Graphical Methods
for Describing Data
Graphs for
categorical data
Double Bar Charts
When to Use
Categorical data
How to construct
Constructed like bar charts, but with two (or
more) groups being compared
MUST use relative frequencies on the
ve
Introduction
The data set that I found is about the relationship between the percentage of body fat and
various predictors taking a sample of 248 men. These predictors include percent body fat
(using another method of calculation), weight, height, adiposi
MAT3375 (Fall 2010)
Assignment 2
Due date (Assignment 2): 10 November 2010
Q1. (3 points) Let rXY ne the sample correlation coecient between X and Y :
rXY =
SXY
.
SXX SY Y
Let Z = aX + b, a > 0. Show that rZY = rXY .
Solution to Q1:
We show rst that SZY
MAT3375 Project 1
Analyze the relationship between the production time in hours and the production lot
size.
Yi Xing #5359701
a)
Program:
DM "OUTPUT" clear;
DM "LOG" clear;
DATA MAT3375.production;
INPUT size hours;
DATALINES;
;
RUN;
dm "output" clear;
dm