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
Lab #1 Introduction to the
Vascular Plant Body
Lab Section
40% of your final grade
10% lab worksheets (8 total)
10% quizzes (3 total)
10% lab report (1)
10% lab exam (1)
Attendance is mandatory
Hand-outs and textbooks will be helpful
No make up missed act
176 Chapter 4 Continuous Variables and Their Probability Distributions
THEOREM 4.6
Proof
4.38
4.39
4.40
4.41
4.42
4.43
4.44
If 91 < (92 and Y is a random variable uniformly distributed on the interval
(01, 92), then
9 9 a a 2
n=E(Y)= 1+ 2 and a2=V(Y)=
364 Chapter 7 Sampling Distributions and the Central Limit Theorem
Even when the population variances are equal, the probability that the ratio of
the sample variances exceeds 3.48 is still .05 (assuming sample sizes of m = 6 and
112 = 10). I
7.9
7.10
4.93
4.94
4.95
4.96
4.97
4.98
4.99
Exercises 1 91
the cost C of completing this operation to the square of the time to completion. Find the mean
and variance of C.
Historical evidence indicates that times between fatal accidents on scheduled American do
m
4.8
4.9
4.10
4.11
4.12
Exercises 167
b Use Table 1, Appendix 3, to obtain P(2 < Y 5 5) and P(2 5 Y _<_ 5). Are these two
probabilities equal? Why or why not?
c Earlier in this section, we argued that if Y is continuous and a < b, then P(a < Y < b) =
P(a 5
Shelter, Housing and Recovery: A
Comparison of U.S. Disasters
ROBERT BOLIN AND LOIS STANFORD
In this paper we examine the issues associated with the tempora y sheltering and
housing of victims after natural disasters in the United States. Specific topics
232 Chapter 5
Multivariate Probability Distributions
5.1
5.2
5.3
5.4
distributions of the populations of joint Observations (y1, y2, . . . , y,) for the discrete
case and the continuous case, respectively. In the continuous case,
P(YtEYI,Y2Ey2,~.-,YnSyiz)
112 Chapter 3 Discrete Random Variables and Their Probability Distributions
3.46
3.47
3.48
3.49
3.50
3.51
3.52
3.53
Construct probability histograms for the binomial probability distributions for n : 5, p = .1,
.5, and .9. (Table 1, Appendix 3, will red
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
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
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
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)
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
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
:6. m. 85.
scan2.2. 2. 05 .= moo. 33. EB 35. uEEam u. 2. b=EanoE u.E.o.&. u. 5.
2:5; .=o_.uc.uu.m 323. u. .8. .2. m2. 3. .225. o. 2. .33. 3.3.: u. 2.
23.22. 3:252. a. wag.3. 2.: .5. 05.53 c. u_pnca2 mm ._ .38 was. m. 35233.
5. an. .6 35. 29. a. = 5.56 .32