Saturday, February 4, 2012
Page 1
Mathematics 1228B
Test 1
CODE 111
PART A (17 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
CODED ON THE SCANTRON SHEET. ALSO CIRCLE YOUR ANSWERS
IN THIS
Mathematics 1228A Assignment 1
(Due by 12 noon EDT Friday May 22, 2015)
Reminder: You must show sucient work to justify your answers.
1. Consider the set containing all rst year students at UWO. Let S
1
Math 1228A - Summer 2015
Assignment 1 Solutions
Question 1
We are thinking in this question only about rst year students at UWO. We have sets S and C which contain
all the students who are taking an
Math 1228A/B Online
Lecture 1:
Using Sets
(text reference: Section 1.1, pages 1 - 2)
c V. Olds 2008
1
Techniques of Counting
Counting seems pretty basic. What were going to be learning about is how to
Extra Practice Questions for Section 1.1
1. Let T be the set of all people who subscribe to TV Guide, M be the set of all people who
subscribe to Macleans magazine, and N be the set of all people who
176
4
CONTINUOUS RANDOM VARIABLES
Example 4.8. (c) P r[0.50 < Z < 0.50]
Once again, we will need to use symmetry and also complementation.
P r[0.50 < Z < 0.50] = P r[Z < 0.50] P r[Z < 0.50]
= P r[Z <
182
4.4
4
CONTINUOUS RANDOM VARIABLES
Approximately Normal Discrete Random Variables
(Note: Thats not the title the text uses for this section.)
Many discrete r.v.s are approximately normal. What does
Saturday, February 4, 2012
Page 1
Mathematics 1228B
Test 1
CODE 111
PART A (17 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
CODED ON THE SCANTRON SHEET. ALSO CIRCLE YOUR ANSWERS
IN THIS
Saturday, February 2, 2013
Page 1
Mathematics 1228B
Test 1
CODE 111
PART A (18 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
CODED ON THE SCANTRON SHEET. ALSO CIRCLE YOUR ANSWERS
IN THIS
1
Math 1228B Final Exam, April 22 2013
Answers Code 111
Part A
1.
A
6.
A
11. E
16. B
21. B
26. E
31. B
2.
7.
12.
17.
22.
27.
32.
E
C
B
B
A
C
C
3.
8.
13.
18.
23.
28.
33.
D
E
C
D
E
B
A
4.
9.
14.
19.
24.
1
Math 1228B Final Exam, April 16 2014
Answers Code 111
Part A
1.
B
6.
D
11. C
16. E
21. B
26. D
31. D
2.
7.
12.
17.
22.
27.
32.
C
A
B
E
A
C
D
3.
8.
13.
18.
23.
28.
33.
D
C
B
D
A
E
E
4.
9.
14.
19.
24.
April 16, 2014
Page 1
Mathematics 1228B
Final Examination
CODE 111
PART A (35 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
CODED ON THE SCANTRON SHEET. ALSO CIRCLE YOUR ANSWERS
IN THIS
April 16, 2014
Page 1
Mathematics 1228B
Final Examination
CODE 111
PART A (35 marks)
A1. On a January morning, it was noticed that exactly 75 of the 100 people waiting at a certain bus stop were
weari
1
Math 1228B Test 2, March 2014
Answers Code 111
Part A
1.
E
7.
A
13. A
2.
8.
14.
B
E
D
3.
9.
15.
C
B
B
4.
10.
16.
D
D
E
5.
11.
17.
E
A
C
6.
12.
18.
C
D
B
Part B
19. (a)
20.
4/10 B
B r
4/10
rr
6/10 R
186
4
CONTINUOUS RANDOM VARIABLES
Approximating the Binomial Distribution
Recall: A random variable X which counts the number of successes in a series of n
Bernoulli trials in which the probability of
4.3 Normal Random Variables
179
Example 4.11. (e) Find a probability expression in terms of X which corresponds to P r[1 < Z < 2].
Since Z =
X25
5 ,
then if Z > 1, we have
X 25
> 1 X 25 > 5 X > 30
5
(
166
4
CONTINUOUS RANDOM VARIABLES
Theorem: Let X be a discrete r.v. whose possible values are evenly spaced k units
apart, and let continuous r.v. Y be a good approximation for X. Let FX (x) and FY (y
3.3 The Mean and Standard Deviation
137
in which the probability of success is p = 1/6 each time. Therefore we have X = B(300, 1/6). Of
course, the mean of X = B(300, 1/6) is given by
= np = 300
1
6
2.7 Independent Trials
113
Let E1 , E2 and E3 be the events that a type 1 urn, a type 2 urn or a type 3 urn is chosen,
respectively. We dont know how many urns there are, but we do know the percentage
3.1 Probability Distributions and Random Variables
121
There are certain properties which a cumulative distribution function, F (x), must always have.
You will have noticed some of these already, whil
Math 1228A/B Online
Lecture 25:
Independence of rvs and
The Joint Distribution of X and Y
(text reference: Section 3.4, pages 136 - 139)
c V. Olds 2008
146
3.4
3 DISCRETE RANDOM VARIABLES
Independent
150
3 DISCRETE RANDOM VARIABLES
Notice: In the joint distribution table, the sum of all the entries in (the main body of) the table is
1. And the probabilities we already lled in sum to 1, so all the
3.4 Independent Random Variables
153
sample point
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
x
1
1
1
1
0
0
0
0
y
2
1
1
0
2
1
1
0
w = xy
2
1
1
0
0
0
0
0
5
1
Of course, since each sample point occurs with probabil
157
4
Continuous Random Variables
4.1
Probability Density Functions
We dened a discrete random variable to be one which has a nite number of possible values. Some
r.v.s can take on any real value, per
3.1 Probability Distributions and Random Variables
127
Next, consider the following:
Fact: Selecting a small random sample from a very large population can be considered
as performing independent tria
140
3 DISCRETE RANDOM VARIABLES
Therefore we need to nd E(X) and (X). (We could nd the pdf of Y and nd E(Y ) and (Y )
directly, but the calculations for E(X) and (X) are easier, i.e. involve easier nu
Math 1228A/B Online
Lecture 29:
The Standard Normal Random Variable Z
(text reference: Section 4.2)
c V. Olds 2008
172
4.2
4
CONTINUOUS RANDOM VARIABLES
The Standard Normal Random Variable
There is a
4.1 Probability Density Functions
163
The width of the rectangle and the base of the triangle are both given by 3 1 = 2. The height
1
of the rectangle is f (1) = 1 . The height of the triangle is the
Saturday, March 15, 2014
Page 1
Mathematics 1228B
Test 2
CODE 111
PART A (18 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
CODED ON THE SCANTRON SHEET. ALSO CIRCLE YOUR ANSWERS
IN THIS B
Chemistry 2374A - Thermodynamics
MIDTERM EXAM 2014 PRACTICE EXAM FOR 2016
(for answers, see last page)
TIME: TWO HOURS
INSTRUCTIONS:
This exam contains 20 questions of equal weight.
A periodic table,
1
4.3
Normal Random Variables
Question 1
We have X being a normal random variable with = 5 and = 1. We know
that X is related to the standard normal random variable Z by the relationship
Z = X
.
(a)
Math1228BSection003
Winter2017
Examples Used In Class
Chapter 4
Example 4.1
A continuous random variable X has the probability density function given by
f(x) = .1 for 0 < x < 10 and f(x) = 0 otherwise