CHAPTER 4
Probability
Multiple-Choice Questions
QUESTIONS 1 THROUGH 11 ARE BASED ON THE FOLLOWING INFORMATION:
Suppose you roll a pair of dice. Let A be the event that you observe an even number. Let B be
the event that you observe a number greater than s
ECO3150
Introduction to Probability and Statistics
David Gray
Fall 2014
There are two parts to this examination one with written questions and one with
problems to solve. There are a total of 100 points. Explain your work and show
your calculations. You c
Probability and Statistics: In the realm of social sciences, management sciences and natural
sciences, theres an element of UNCERTAINTY (dont know what events are going to occur or
what is going on exactly). Economists are investigating things we dont tot
Chapter 1
You can safely ignore the following topics and items:
Nominal data
Pareto diagram
Stem-and-leaf display
Appendix
You should concentrate on the following topics and items:
Population
Sample
Random sample
Parameter
Statistic
Qualitative data
Quant
ECO3150 - Introduction to Probability and Statistics
University of Ottawa
David Gray
Fall 2015
Second formal assignment
Carefully prepare written responses to the following questions. This entails not
only the mathematical exposition, but also some writte
David Gray
Fall 2015
Third Formal Assignment
Carefully prepare written responses to the following questions. The exposition of
your solutions comprises an important part of this exercise. You can certainly
work in groups, but it is imperative that you wri
ECO3150 - Introduction to Probability and Statistics
University of Ottawa
David Gray
Fall 2015
Second Midterm Examination
There are two parts of this examination: one consisting of problems, and one
consisting of written questions. Explain your work and s
ECO3150
Introduction to Probability and Statistics
David Gray
Fall 2015
First midterm examination
There are two parts of this examination: one consisting of problems, and one
consisting of written questions. Explain your work and show your calculations.
Y
In the realm of special science, management science, medical research, and natural
science. Theres almost always, an element of uncertainty. Where by certain
event/outcome may or may not occur. We measure this likelihood using a metric
called probability
ECO3150
2014
Fall
David Gray
Solutions to first midterm examination
For questions # 1 through 5, see the excel file.
# 6: This question was taken from the exercises in the textbook. The answer is posted on the
courseweb: chapter 3, document containing the
Question # 1
X
0
1
Y
marg. P (X)
E (X)
E (Y)
COV (X,Y)
1.6
0.4
-0.24
1
0
0.4
0.4
2 marg P (Y)
0.6
0.6
0
0.4
0.6
Var (X)
Var (Y)
corr.
coeff (X,Y)
f) They are not statistically
independent. Instead, there is a
perfect negative correlation
between the two v
ECO3150 - Introduction to Probability and Statistics
University of Ottawa
David Gray
Fall 2014
Second Midterm Examination
There are two parts of this examination: one consisting of problems, and one
consisting of written questions. Explain your work and s
Statistics for
Business and Economics
8th Edition
Chapter 6
Sampling and
Sampling Distributions
ECO3150 OU
Ch. 6-1
Chapter Goals
After completing this chapter, you should be able to:
Describe a simple random sample and why sampling is
important
Explain
PART A - the breakdowns themselves
# of breakdowns
probability
# of breakdowns* probability
0
0.1
0
1
0.26
0.26
2
0.42
0.84
3
0.16
0.48
4
0.06
0.24
E (# of breakdowns)
1.82
Note that the cost of breakdowns = $1,500 *
the number of breakdowns
PART B - the
Question # 1
X
0
1
Y
marg. P (X)
E (X)
E (Y)
COV (X,Y)
1.6
0.4
-0.24
1
0
0.4
0.4
2 marg P (Y)
0.6
0.6
0
0.4
0.6
Var (X)
Var (Y)
corr.
coeff (X,Y)
f) They are not statistically
independent. Instead, there is a
perfect negative correlation
between the two v
#1
brokerage house
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
100 transactions 500 transactions 100 transactions sorted
30
29.95
24.99
10.99
54
24.95
17
5
55
29.95
12.95
9.95
49.95
14.95
35
19.75
25
15
40
20
39
62.5
9.95
10.55
50
29.95
45
14.95
24
14
Pie Charts show relative frequencies, which are easily derived from raw
frequencies. Divided those raw frequencies by the number of observations, which
generate decimals between 0 and 1. These relative frequencies sum to 1, 0.
Time Series Data
Think of an
10-11am DMS 9161 tomorrow followed by OH.
Chapter 2 Describing Statistics Numerical
Given a sample of an observations for some variable, we seek to summarize it.
Commence with measure of central tendency
Population mean
Sample mean
Median: place all of th
Range: different between the min and the max value, the greater the distance, the
greater the dispersion involves only 2 values.
Quartiles: 4 quartiles to any distribution. First sort the values top quartile 75% tile
and above. Second quartile 50%tile (me
Home Assignment 1
Probability and Statistics for Economists ECO3150C
Instructor: Rachidi KOTCHONI
N.B. Please submit your assignment by October 9 th , 2014. May be done in teams of no more than two
students. Plagiarism will not be tolerated.
Exercise 1. (
Home Assignment #2
Probability and Statistics for Economists ECO3150C
Instructor: Rachidi KOTCHONI
N.B. Please submit your assignment by November 24 th , 2014. May be done in teams of no more
than two students. Plagiarism will not be tolerated.
Exercice 1
PROBABILITY AND STATISTICS FOR ECONOMISTS (3150)
Fall 2016
6. Sampling and Sampling Distribution
Cristina Blanco-Perez
Facult des sciences sociales | Faculty of Social Sciences
uOttawa.ca
Outline
1. Sampling Distribution
2. Sample Distribution of Sample M
PROBABILITY AND STATISTICS FOR ECONOMISTS (3150)
Fall 2016
5. Continuous Random Variables and Probability Distributions
Cristina Blanco-Perez
Facult des sciences sociales | Faculty of Social Sciences
uOttawa.ca
Outline
1. Continuous random variables
2. So
PROBABILITY AND STATISTICS FOR ECONOMISTS (3150)
Fall 2016
3. Probability
Cristina Blanco-Perez
Facult des sciences sociales | Faculty of Social Sciences
uOttawa.ca
Outline
1. Basic concepts (plus slides lesson03.1)
2. Probability
3. Probability Rules
4.
PROBABILITY AND STATISTICS FOR ECONOMISTS (3150)
Fall 2016
2. Describing Data: Numerically
Cristina Blanco-Perez
Facult des sciences sociales | Faculty of Social Sciences
uOttawa.ca
Outline
1. Describing Data: numerically
2. Measures of central tendency
3