Answer all three questions below in a word processed document.
1. What are the differences between the neoclassical and structural evolutionary
theories of economic growth? Articulate each theory clearly and point out the
differences. What are the implica
NOVEMBER 24, 2014
LECTURE 14
CONDITIONAL DISTRIBUTIONS AND EXPECTATIONS
1
Conditional distributions
Recall that we previously dened the conditional probability of an event A given another event
B as
P (A|B) =
P (A \ B)
P (B)
when P (B) > 0. The conditiona
NOVEMBER 19, 2014
LECTURE 13
COVARIANCE AND CORRELATION
1
Expectations with bivariate distributions
In the previous lecture, we extended the concept of distributions from the one-variable scenario
to multivariate (bivariate) distributions. One can similar
Econ 327
Assignment 9
The due date for this assignment is Thursday November 20.
1. Exercises 4.1-1. 4.1-2, 4.1-3, 4.1-4 on pages 133 of Hogg, Tanis and Zimmerman.
2. Let X and Y be two random variables each taking two values, zero or one.
(a) Specify a jo
Econ 327
Assignment 10
The due date for this assignment is Thursday November 27.
1. Exercises 4.2-1, 4.2-2, 4.2-6, 4.2-7 on page 139 of Hogg, Tanis and Zimmerman.
2. Exercises 4.4-1, 4.4-2, 4.4-4 on page 153.
3. (a) Show that V ar(X1 +X2 +X3 ) = V ar(X1 )
Anton Laptiev
ECON 327: Solution to Problem Set #6
November 5, 2014
Problem 2.3-13
The probability of the event cfw_rst three answers are incorrect, forth answer is correct given the random
selection of answers (and thus, independence) equals 0.83 0.2 0.1
Anton Laptiev
ECON 327: Solution to Problem Set #7
November 20, 2014
Problem 3.1-3
a) We have uniformly distributed random variable with support (0,10). Therefore, the pdf of X is
1/10, with 0 < X < 10.
b) P (X 8) =
10
8
1/10 dx = x/10 |10 = 0.2.
8
c) P (
Anton Laptiev
ECON 327: Solution to Problem Set #8
November 23, 2014
Problem 3.3-1
a) P (0.53 < Z 2.06) = (2.06) (0.53) = 0.98030 0.70194 = 0.27836
b) P (0.79 Z < 1.52) = (1.52) (0.79) = 0.93574 0.21476 = 0.72098.
c) P (Z > 1.77) = P (Z < 1.77) = 0.96164.
Anton Laptiev
ECON 327: Solution to Problem Set #9
November 24, 2014
Problem 4.1-1
a)
b)
f (x, y) = c 33 = c =
1
33
f (x, y) = c 24 = c =
1
24 .
c) We have three xs for each y=cfw_0,1,2,3,4,5. Overall 18 possible combinations. Thus,
1
18 c = c = 18 .
( 1
Anton Laptiev
ECON 327: Solution to Problem Set #11
December 1, 2014
Problem 4.3-6
a)
fX (x) = P (X = x) =
f (x, y) = P (X = 500) =
y
P (Y = 500) =
P (X = 500, y) = 0.4
y
P (x, Y = 500) = 0.35
x
P (Y = 500|X = 500) =
P (X = 500, Y = 500)
= 0.5
P (X = 500)
Econ 327
Practice questions for the nal exam
1. Exercises 2.4-8, 2.4-17, 2.4-19 on page 73.
2. Exercises 2.6-1, 2.6-4, 2.6-6 on page 85.
3. Find the limit of (n 1)/n)n as n .
4. Exercises 3.1-2, 3.1-8, 3.1-14 on pages 93-94.
5. Suppose that X U nif orm(4,
UBC, ECONOMICS 327
2014 MIDTERM EXAMINATION
Suggested solution
1. (A B) (A B)c .
2.
Note that A3 and A3 are identical. Hence, we just need to show that A1-A3
imply A1 and A2 , and that A1 -A3 imply A1 and A2.
To show that A1-A3 imply A1 , by Axiom A3 P
NOVEMBER 13, 2014
LECTURE 12
JOINT (BIVARIATE) DISTRIBUTIONS, MARGINAL DISTRIBUTIONS,
INDEPENDENCE
So far we have considered one random variable at a time. However, in economics we are
typically interested in relationships between several variables. There
Technology and technological
Change
Chapter 4
The Micro economics of technological
change
The arrow of time and its implications
Technology and scale effects
General purpose technologies
How do we know a GPT when we see one
The microeconomics of
tech
A structuralist-evolutionary
decomposition
Chapter 3
The S-E decomposition
Six main categories
Technology
Facilitating structure
Inputs
Public policy
Policy structure
Performance
Technology
Cambridge encyclopaedia version:
The use of tools, machines, m
The take off into sustained
growth
Chapter 7
Introduction
We have seen the growth sustaining
effects of several GPTs in history.
However, the growth that started
sometime in the 19th century is much more
rapid than anything that has been seen
previously
The neoclassical model of
economic growth is not
sufficient to explain sustained
economic growth driven by
technoilogical change
The neoclassical model
of economic growth is not
sufficient to explain sustained
economic growth driven by
technoilogical chan
GENERAL PURPOSE TECHNOLOGIES IN THEORY, APPLICATIONS
AND CONTROVERSY: A REVIEW
by
Clifford Bekar, Kenneth Carlaw, Richard Lipsey
Contacts
Clifford Bekar: bekar@lclark.edu
Kenneth Carlaw:Kenneth.Carlaw@ubc.ca
Richard Lipsey: rlipsey@sfu.ca
Abstract
The two
OCTOBER 13, 2014
LECTURE 7
EXAMPLES OF DISCRETE DISTRIBUTIONS
In this lecture, we consider some common examples of families of discrete distributions:
collections of PMFs described by one or more parameters.
1
Bernoulli trials
This is probably the simples
OCTOBER 22, 2014
LECTURE 8
CONTINUOUS RANDOM VARIABLES AND PROBABILITY DENSITY
FUNCTIONS (PDFs), UNIFORM DISTRIBUTION
The theory of discrete distributions and random variables described in previous lectures is
very useful in many situations. However, ther
OCTOBER 29, 2014
LECTURE 10
QUANTILES (PERCENTILES), SYMMETRIC DISTRIBUTIONS, LOGISTIC
DISTRIBUTION
1
Denition and properties
Let X be a continuously distributed random variable with a CDF FX . Suppose that the CDF
function is monotone increasing everywhe
OCTOBER 31, 2014
LECTURE 9
EXPECTATION OF A CONTINUOUSLY DISTRIBUTED RANDOM
VARIABLE, DISTRIBUTION FUNCTION AND CHANGE-OF-VARIABLE
TECHNIQUES
1
Expectation of a continuously distributed random variable
Recall that in the case of a discrete random variable
NOVEMBER 3, 2014
LECTURE 11
NORMAL DISTRIBUTION
The normal distribution is the most important distribution used in statistics. As we will
discuss later in the course, many distributions that arise in practice can be approximated by
the normal distribution
ECONOMICS 309
INTERMEDIATE OPEN ECONOMY MACROECONOMICS
GERALD MCINTYRE, PH.D.
VANCOUVER SCHOOL OF ECONOMICS
UNIV. OF BRITISH COLUMBIA
TERM 2 2014/15
Additional Study Questions for the First Mid-Term, Tuesday, Feb 10th 6 7:30pm
1. In the steady state of th
Name and Student Number: _
Economics 302
Intermediate Macroeconomics
Gerald McIntyre, Ph.D.
Vancouver School of Economics
University of British Columbia
Term 2 2014
First Exam Version A, February 6, 2014
Print your name and student number at the top of th
Chapter 9
The Cutting Edge of Technology
Note: Special icons in the margin identify problems requiring a computer or calculator
requiring calculus .
and those
Solutions to Problems
1.
The annual growth rate of productivity is given by the following equat
Chapter 8
The Role of Technology in Growth
Note: Special icons in the margin identify problems requiring a computer or calculator
.
Solutions to Problems
1.
a.
Nonrival. Nonexcludable. Ones consumption of National Defense does not diminish anothers
consu
Chapter 4
Population and Economic Growth
Note: Special icons in the margin identify problems requiring a computer or calculator
requiring calculus .
and those
Solutions to Problems
1.
To find the average growth rate of the population, we use the followin
CHAPTER 10: INTRODUCTION TO ESTIMATION
TRUE/FALSE
1. An unbiased estimator is said to be consistent if the difference between the estimator and the parameter
grows smaller as the sample size grows larger.
ANS: T
PTS: 1
NAT: BUSPROG.SFME.KELL.15.03
KEY: Bl
CHAPTER 12: INFERENCE ABOUT A POPULATION
TRUE/FALSE
1. In order to determine the p-value associated with hypothesis testing about the population mean , it is
necessary to know the value of the test statistic.
ANS: T
PTS: 1
NAT: BUSPROG.SFME.KELL.15.03
KEY
CHAPTER 15: CHI-SQUARED TESTS
TRUE/FALSE
1. A chi-squared distribution is symmetric.
ANS: F
PTS: 1
NAT: BUSPROG.SFME.KELL.15.03
KEY: Bloom's: Knowledge
DIF: Easy
OBJ: SFME.KELL.15.15.01
STA: DISC.SFME.KELL.15.06
2. A chi-squared test is used to describe a
CHAPTER 16A: SIMPLE LINEAR REGRESSION AND CORRELATION
TRUE/FALSE
1. An inverse relationship between an independent variable x and a dependent variably y means that as x
increases, y decreases, and vice versa.
ANS:
OBJ:
NAT:
KEY:
T
PTS: 1
DIF: Easy
SFME.KE
CHAPTER 14: ANALYSIS OF VARIANCE
TRUE/FALSE
1. The F-test used in one-way ANOVA is an extension of the t-test of 1 2.
ANS: T
PTS: 1
NAT: BUSPROG.SFME.KELL.15.03
KEY: Bloom's: Comprehension
DIF: Easy
OBJ: SFME.KELL.15.14.01
STA: DISC.SFME.KELL.15.09
2. We