EC507Statistics for Economists
Fall 2011
Problem Set 1
1. Two six-sided dice are thrown sequentially, and the face values that come up are
recorded.
a. List the sample space.
b. List the elements that make up the following events:
i. A = the sum of the tw
EC507Statistics for Economists
Fall 2011
Problem Set 4
1. X is a normally distributed random variable with mean equal to 7 and variance
equal to 25. You draw a random sample of size 100.
a. Calculate P (6 X 8) and P(6 X 8) .
67 X 7 87
P (6 X 8) = P
25
25
a) What is the socially optimal quantity of resource extraction in the two periods? This part dthe
question can be satisfactorily answered with a carefully drawn graph. But, in addition. if
you're comfortable using some simple algebra, you can get more pr
1
MULTIVARIATE
PROBABILITY
DISTRIBUTIONS
Statistics for Economists EC 507 A1
2
Introduction
For a given experiment, we are often interested in relationships of two or more random
variables.
For a study of lung cancer, a researcher is interested in the n
1
MULTIVARIATE PROBABILITY
DISTRIBUTIONS PART II
Statistics for Economists EC 507 A1
2
Expected Value of a Bivariate Random Variable
Discrete Case
Definition:
Let
and
function
Let
,
,
be two discrete random variables with the joint probability
, .
be a
1
COUNTING
TECHNIQUES IN
PROBABILITY
Statistics for Economists EC 507 A1
2
Calculating Probability of an Event
Axiomatic definition of probability states only the conditions an assignment of
probabilities must satisfy, but it does not tell us how to assi
1
SPECIAL CONTINUOUS
DISTRIBUTIONS
Statistics for Economists EC 507 A1
2
Special Continuous Distributions
Uniform distribution on an interval
Normal distribution
Exponential distribution
Gamma distribution
Chi-square distribution
3
Uniform Distributi
1
INTRODUCTION TO
PROBABILITY
Statistics for Economists EC 507 A1
2
Introduction
After the data is described and summarized, we hope to be able to
draw a conclusion on a question of interest.
The part of statistics concerned with the drawing of conclusi
EC507Statistics for Economists
Fall 2011
Problem Set 6 Solutions
Problem 1: Suppose some data on the calorie content of beef hot dogs is given. Here are the numbers of
calories in 20 different hot dog brands:
186, 181, 176, 149, 184, 190, 158, 139, 175, 1
EC507Statistics for Economists
Fall 2011
Problem Set 6
Problem 1: Suppose some data on the calorie content of beef hot dogs is given. Here are the numbers of calories in 20
different hot dog brands:
186, 181, 176, 149, 184, 190, 158, 139, 175, 148,
152, 1
EC507Statistics for Economists
Fall 2011
Problem Set 5 Solutions
1. You run a survey of n professors across Illinois. Youre interested in estimating the mean
salary for the population of college professors in Illinois based on the salary data from
your su
EC507Statistics for Economists
Fall 2011
Problem Set 5
1. You run a survey of n professors. You estimate the mean salary for the population
of professors based on salary data from the survey, S1, S2, Sn. Two estimators
~
S + 1.1S 2 + .9 S3
S + S 2 + S3
~
EC507Statistics for Economists
Fall 2011
Problem Set 4
1. X is a normally distributed random variable with mean equal to 7 and variance
equal to 25. You draw a random sample of size 100.
a. Calculate P (6 X 8) and P (6 X 8) .
b. Explain intuitively why th
EC507Statistics for Economists
Fall Spring 2011
Problem Set 3
Let the random variable X denote a persons weight (normalized so that the max weight is
1). And let the random variable Y denote a persons life expectancy (also normalized so
that the domain of
EC507Statistics for Economists
Fall Spring 2011
Problem Set 3
Let the random variable X denote a persons weight (normalized so that the may weight is
1). And let the random variable Y denote a persons life expectancy (also normalized so
that the domain of
EC 507Statistics for Economists
Fall 2011
Problem Set 2 Solutions
1. Acme Insurance Co. is considering entering the market for freak accident insurance.
The CEO of Acme wants you to head the new group to develop products to insure
individuals against seve
EC507Statistics for Economists
Fall 2011
Problem Set 2
1. Acme Insurance Co. is considering entering the market for freak accident
insurance. The CEO of Acme wants you to head the new group to develop
products to insure individuals against severely biting
EC507 Statistics for Economists
Fall 2010
Problem Set 1
1. Two six-sided dice are thrown sequentially, and the face values that come up are
recorded.
a. List the sample space.
= cfw_(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2