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)
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
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
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
GENERAL PURPOSE TECHNOLOGIES IN THEORY, APPLICATIONS
AND CONTROVERSY: A REVIEW
by
Clifford Bekar, Kenneth Carlaw, Richard Lipsey
Contacts
Clifford Bekar: [email protected]
Kenneth Carlaw:[email protected]
Richard Lipsey: [email protected]
Abstract
The two
Assignment #2 based on Ch.3 and Ch.4
Draw a diagram similar to the one for Solow Model for Harrod _Domar Model
clearly outlining the difference.
What is the significance of the concave shape of the production fu
Assignment #3 based on Ch.8
What is Creative destruction?
What are the factors that induce firms to invest in R & D?
What are the pros and cons of the patent system?
A1 and A2 represent the levels of tec
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
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 Answers for the First Mid-Term, Tuesday, Feb 10th 6 7:30pm
1. In the steady sta
Announcements
Today:
Fri:
Mon:
Wed:
Chinas large na2onal saving
Solow model with Technological Change; Chp. 12
Growth of key Variables
Cross-County Convergence
Problem Set 2 due
Announcements
Today:
Solow model with Technological Change; Chp. 12
Growth of key Variables
Cross-County Convergence
TFP and the Solow Residual
Problem Set 2 due Sunday, Jan 25 at 11pm on MyEconLab
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 3
Physical Capital
Note: Special icons in the margin identify problems requiring a computer or calculator
requiring calculus .
and those
Solutions to Problems
1.
The key characteristics of physical capital are that it is productive, it is produce
SEPTEMBER 3, 2014
LECTURE 2
CONDITIONAL PROBABILITY, INDEPENDENCE, BAYES RULE
1
Conditional probability
The probability model is concerned with evaluating the likeliness of events. However often
when evaluating the likeliness of events, researchers need t
SEPTEMBER 15, 2014
LECTURE 1
BASICS OF PROBABILITY
1
Uncertainty or why we need probability and statistics
Many important economic models are concerned with decision making under uncertainty. For
example:
The investors decision to buy or sell stocks invo
Econ 327
Practice questions for the final exam
1. Suppose that X U nif orm(4, 9), and let Y =
X.
(a) Find the support, the CDF, and the PDF of the distribution of Y .
(b) Find EY and V ar(Y ).
(c) Find the three quartiles of the distribution of Y .
2. Sup
Risk Management: Course Summary
Professor Philippe Jorion
May 2013
Goals of risk management:
Understanding the risk profile of the entire portfolio for better risk/return positioning (typically, a large-scale problem)
This requires identification and me
The dream machine - Ten years ago a group of young bankers had a weekend away in
Boca Raton. In between throwing each other in the pool, and a lot of drinking, they
invented something that changed the world of finance.
By GILLIAN TETT, 4719 words
25 March