Econ 7818
Problem Set #2
Distributed: 9/3
Due: 9/10
1. (text exercise 9 p. 18).
2. Suppose the random variables \ ] have joint distribution
0 B C B C ! B " ! C "
a. Prove that this is a proper probability distribution (i.e. satisfies the axioms of
probabi
Problem Set #7
Due Thursday, 10/29
Chapter 7 Problems
1.
Choose any three of 2, 6, 7, 8, 11, or 12, pps. 151 - 2;
2.
Choose any three of 15, 18, 19, or 21, pps. 154 - 5.
Problems 15, 18, and 19, and maybe others, are examples where the regularity conditio
ECON 7818
Problem Set 8
Suggested Solutions
1. (7.6, p. 152) Let X1 , X2 , and X3 be independent binary random variables taking
and
1 with probability p and 0 with probability 1 p. Define two estimators p1 = X
p2 = (X/2) + (1/4), where X = (X1 + X2 + X3
ECON 7818
Problem Set 7
Suggested Solutions
1. Let X1 , . . . , Xn be independent with exponential distribution with parameter . Find two different method of moments estimators of .
Well,
f (x) = ex ,
x>0
So,
Z
E(X) =
xf (x) dx
0
Z
xex dx
=
0
We can now i
Suggested solutions - Exercises Chapter 7 up to ML Estimation
2.
6.
s "\
Since I \ "- s #8" \3#
Since I \ # #-# , Similarly, since Z \ "-# , one could use "=, where = is the sample st. dev.
For s:" B, we have I s:" : Z s:" :" :$ Q WI s:"
For s:# B# "#, w
Econ 3818
1.
Midterm I
Consider the random variable \ :
\
T \
a.
b.
c.
d.
Suggested Solutions
!
5
#
$
%
"
6
.1
Is this random variable discrete or continuous (circle one)?
Find T \ $
T \ $ 0.8 .
Find I \ , the expected value of \ .
I \ 1.6 .
A friend say