Problem Set #8

Solutions
14.30  Intro. t o Statistical Methods in Economics
Tnst,ri~ctor: onrwd Menzel
K
Due: Tuesday, April 28, 2009
Question One: Law of Large Numbers and Central Limit
Theorem
Probably the two most important concepts that you will ta
14.30 Exam 2 Solutions
Fall 2004
Bilal Zia
RR
1 A:
a)
E(aX + bY + c) = aE(X) + bE(Y ) + c
ZZ
RR
RR
(aX + bY + c)fX,Y (x, y)dxdy =
aXfX,Y (x, y) +
bY fX,Y (x, y) +
cfX,Y (x, y)
R
R
R
R
R
= aX fX,Y (x, y)dy dx + bY
fX,Y (x, y)dx dy + c = aXfX (x) +
R
bY fY
Exam 3
MIT 14.30 Spring 2006
Herman Bennett
Instructions: This exam is closedbook and closednotes. You may use a simple calculator.
Please read through the exam in order to ask clarifying questions and to allocate your time
appropriately. You must show
Problem Set #1
14.41 Public Economics
DUE: September 24, 2010
1
Question One
For each of the examples below, please answer the following:
1. Does an externality exist? If so, classify the externality as positive/negative (or both).
2. If an externality ex
gm;
@ grade, Frouxston ONij max U; 41,461); (HQ/(M53
{6,53
l. Mame maximizes (ANNE b3 SOME/g git. 6+ FEE éw
me UH 1:3 maximizwon Hwomj) wa know UHHJ :3 maxmfzed when
m magmd mire GP subs+1+uon is equal 41: +he Price, m41o) and
when aU monej In 1% buogd ?S
14.30 EXAM 2  SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Question 1
A.
(i)
F alse. The result E (g (X) = g (E (X) only holds for linear
functions of X, because integration is only distributive over linear functions.
R1
R1
(ii)
F alse.
1 h (x) fX (x) dx = E
Exam 2
14.30 Fall 2004
Herman Bennett
Instructions: This exam is closedbook and closednotes. You may use a simple calculator.
Please read through the exam in order to ask clarifying questions and to allocate your time
appropriately. You must show all your
Problem Set #3
14.41 Public Economics
DUE: October 29, 2010
1
Social Security
DIscuss the validity of the following claims about Social Security. Determine whether each claim is
True or False and present a concise explanation for your answer:
1. Social se
Exam 2
MIT 14 30 Spring 2006
Herman Bennett
Instructions: This exam is closedbook and closednotes. You may use a simple calculator.
Please read through the exam in order to ask clarifying questions and to allocate your time
appropriately. You must show
Problem Set #9
14.30  Intro. to Statistical Methods in Economics
Instructor: Konrad Menzel
Due: Friday, May 8, 2009
Question One: Confidence Intervals
(Adapted from BainIEngelhardt p. 384)
Consider a random sample of size n from a normal distribution, Xi
14.30 EXAM 3  SUGGESTED ANSWERS
TA: Tonja Bowen Bishop
Question 1
(i)
F alse=U ncertain. MLE produces estimators that are consistent, but may or may not be unbiased.
(ii)
F alse=U ncertain. MM estimators may be biased or unbiased, consistent or inconsist