Econ-240A (1st Half - Fall 2013)
Problem Set 1 - Solution
Due: Friday, September 16th
Exercise 1. If F is both a -system and a -system, then it is also a -algebra.
Solution 1. We need to show the following three properties:
1. F,
2. A F implies Ac F, and
Econ-240A (1st Half - Fall 2013)
Problem Set 2
Due: Monday, September 23rd
Exercise 1 ( Inequalities) Prove the following inequalities:
1. (Location-scale Inequality) Let X be a random variable with E X 2 < . Dene = E [X],
2 = Var [X], and m = M edian [X
Problem Set 1
Econ 240A - Second Half
Raaele Saggio
University of California, Berkeley
November 3, 2013
Please send me an email in case you spot any typos: [email protected]
1
1.1
We can apply the transformation theorem for the multivariate
Economics 240A - 1st half
Fall 2015
Problem Set 1
(Due September 16, 2015)
Exercise 1. Let (, F, P) be a probability space. Show that
a) If A, B F, then A B F.
b) Can we have that A B and A B?
c) If An F for all n N, then
An
P
n=1
n=1
P (An ).
d) If An A,
Ec240a, Fall 2013
Professor Bryan Graham
Problem Set 1
Due: October 28th 2013
Problem sets are due at 5PM in the GSIs mailbox. You may work in groups, but each student should turn
in their own write-up (including individually commented and executed code i
Solutions Manual for
Statistical Inference, Second Edition
George Casella
University of Florida
Roger L. Berger
North Carolina State University
Damaris Santana
University of Florida
0-2
Solutions Manual for Statistical Inference
When I hear you give your
Ec240a, Fall 2015
Professor Bryan Graham
Problem Set 1
Due: October 26th, 2015
Problem sets are due at 5PM in the GSIs mailbox. You may work in groups, but each student should turn
in their own write-up (including a printout of a narrated/commented and ex
Economics 240A - 1st half
Fall 2015
Problem Set 1
Suggested solutions
Exercise 1. Let (, F, P ) be a probability space. Show that
a) If A, B F, then A B F.
b) Can we have that A B and A B?
c) If An F for all n N, then
An
P
n=1
n=1
P (An ).
d) If An A, the
Economics 240A - 1st half
Fall 2015
Problem Set 3
Suggested solutions
Exercise 1. Let X Rn be a random sample. Suppose X1 poisson() where 0 is unknown.
a) Show that
n
i=1 Xi
is a sucient statistic for .
b) Find the method of moments estimator and maximum
Economics 240A - 1st half
Fall 2015
Problem Set 4
Suggested solutions
Exercise 1. Let X Rn be a random sample with X1 U [0, ] where > 0 is unknown. Consider
the hypotheses testing problem
H0 : 1
vs.
H1 : > 1,
and the test which rejects H0 when X(n) > c.
a
Economics 240A - 1st half
Fall 2015
Problem Set 2
Suggested solutions
Exercise 1 (Applications of Jensens inequality).
a) Let X be a random variable with E[X 2 ] < . Write = E[X], 2 = Var(X), and m for a
median of X. Show that
| m|
Hint: You can use that
How do you Open Happiness?
Coca-Cola was formulated in 1886 by
pharmacist John Pemperton who sold the
product at drug stores as potion for mental
and physical disorders.
However, the war started more then a
centaury ago
At the late 90s
US per capita went
Economics 240A
Fall 2012
Midterm Exam
(October 10, 2012)
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please
Economics 240A
Fall 2011
Midterm Exam
(October 17, 2011)
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please
Economics 240A
Fall 2013
Midterm Exam
October 16, 2013
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please wr
Economics 240A
Fall 2007
Midterm Exam
October 17, 2007
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please wr
Economics 240A
Fall 2010
Midterm Exam
October 13, 2010
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please wr
Economics 240A
Fall 2009
Midterm Exam
October 14, 2009
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please wr
Economics 240A
Fall 2006
Midterm Exam
October 18, 2006
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please wr
Economics 240A
Fall 2008
Midterm Exam
October 20, 2008
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please wr
Economics 240A
Fall 2003
Midterm Exam
October 14, 2003
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please wr
Economics 240A
Fall 2005
Midterm Exam
October 17, 2005
Instructions: This is a closed book exam, but you may refer to one sheet of notes. You have 80 minutes
for the exam. Answer as many questions as possible. Partial answers get partial credit. Please wr