International Finance Homework 3
Fall 2013
1. Come up with a swap (principal + interest) for two parties A and B who have the
following borrowing opportunities.
The current exchange rate is $1.60 = 1.00. Company "A" wishes to borrow $1,000,000
for 5 years
AMS 312.01
Practice Final Exam #2
Spring, 2010
Name_ID_Signature_ Instructions: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete solutions for full credit. Good luck! 1. In a study of hypnotic su
Solution of AMS312_2010 Practice Mid-term 1
AMS312.01
Practice Midterm Exam #1
Spring, 2010
Instructions: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete solutions for full credit. Good luck! (*
Solutions to Homework #7.
Please note those in red are not required however, if you have time, study them
as they are good candidates for the extra credit problem.
7.1.5
(a)
(b)
(c)
7.1.6
(a)
(b)
7.1.9
7.3.1
2 sided situation:
Under , ,
Under , ,
, and
Th
Power of the test & Likelihood
Ratio Test
<Today s Topic>
Power Calculation (Inference on one population
mean)
Likelihood Ratio Test (one population mean, normal
population)
Truth
Decisio
Type II
n
error
Type I
error
= P(Type II error) = P(Fail to reject
P-value & Power of the Test, Revisited
Example 1.
Bayport High was chosen to participate in a new curriculum program. A
year later, 86 Bayport sophomores who participated in this program was
randomly selected to take a SAT-I math exam. The national averag
AMS 312
Professor Wei Zhu
*1. Review: The derivative and integral of some important
functions one should remember.
*The Chain Rule
For example:
*The Product Rule
*2. MGF, its second function: The m.g.f. will also generate the
moments
Moment: 1st (populati
AMS312 Lecture Notes #4
Review of Probability (continued)
(3)
Normal Distribution
Q. Who invented the normal distribution?
1
* Abraham de Moivre (26 May 1667 in Vitry-le-Franois,
Champagne, France 27 November 1754 in London, England)
*From the Wikipedia
(
AMS312
Quiz 2
Name: _
ID: _
1.
The gunner on a small assault boat fires six missiles at an
attacking plane. Each has a 20% chance of being on target. If
two or more of the shells find their mark, the plane will
crash. At the same time, the pilot of the pl
AMS312 Practice Midterm Exam
Instructions: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F.
Please provide complete solutions for full credit. Good luck!
1. Let , be a random sample from the normal population where both
AMS312
Quiz 3
Name: _ID:
_
This is a close book exam. Anyone who cheats will receive a grade of F for the entire course. Turn in by 12noon. (Use the front/back of this paper to finish your quiz.)
Suppose that the p.d.f. of the random variableis , . Please
AMS312
Quiz 4
Name: _ID:
_
This is a close book exam. Anyone who cheats will receive a grade of F for the entire course. Turn in by 12noon. (Use the front/back of this paper to finish your quiz.)
The conditional distribution of X given Y = y is defined as
AMS312
Quiz 5
Name: _ID: _
A post office has two clerks, Lucy and Ricky. It is known that their service times are two independent exponential
random variables with the same parameter , and it is known that Lucy spends on the average 10 minutes with each
c
Chapter 7
Hypothesis Testing
Example.
(null hypothesis) : the average height is
58 or more.
(alternative hypothesis) : the average
height is less than 58
Example. (law suit) O.J. Simpson case
: O.J. is innocent. (original belief)
: O.J. is guilty.
Truth
D
AMS312
CI, continued
1. Inference on one population variance 2 ,
population is normal (6.4)
1 Point estimator: = s =
2
estimator of
Pivotal
W=
2
1
2
( X i X ) and s 2 is unbiased
n 1
2
Quantity
( n 1) s 2
2
for
the
inference
on
2
(P.Q.):
2
~ n1
2 Confide
AMS 312
Professor Wei Zhu
Jan 24th
1. Review of Probability, the Monty Hall Problem
(http:/en.wikipedia.org/wiki/Monty_Hall_problem)
The Monty Hall problem is a probability puzzle loosely based on the American television game
show Let's Make a Deal and na
January 26th
AMS312
Professor Wei Zhu
1. Review of Probability (continued)
Exercise:
A write to B and does not receive an answer. Assuming that one
letter in n is lost in the mail, find the chance that B received the
letter. It is to be assumed that B wou
AMS312 Lecture Notes #3
Review of Probability (continued)
Probability distributions.
(1)
Binomial distribution
Eg. 1. Suppose each childs birth will result in either a boy or a
girl with equal probability. For a randomly selected family with 2
children, w
AMS312 Lecture Notes #4
Review of Probability (continued)
(3)
Normal Distribution
Q. Who invented the normal distribution?
* Abraham de Moivre (26 May 1667 in Vitry-le-Franois,
Champagne, France 27 November 1754 in London, England)
*From the Wikipedia
* J
AMS 312
Professor Wei Zhu
*Review: The derivative and integral of some important
functions one should remember.
*The Chain Rule
For example:
*The Product Rule
*Review: MGF, its second function: The m.g.f. will also
generate the moments
Moment: 1st (popula
AMS312
Prof. Wei Zhu
Sampling from the normal population
Theorem. Let be a random sample from a normal population .
Then, we have the following:
1.
1.
2. and are independent.
3. Let . Then,
2. Let . Then,
is t distribution with (n-1) degrees of freedom.
D
AMS312
Further Review of Normal Distribution:
Example: , and the value of random variable W depends on a coin
flip: , find the distribution of W. Is the joint distribution of Z and W
a bivariate normal?
Solution:
So .
The joint distribution of Z and W is
Lecture 7.
Cramer-Rao Lower Bound
Unbiased Estimator of , say
It can be really difficult for us to determine which one is the best when
there are many of them.
Theorem. Cramer-Rao Lower Bound
Let be a random sample from a population with p.d.f. Let be an
Lecture 9.
Review: Conditional Distribution:
Example. Let X and Y be random variables with joint pdf where ,
. Then X and Y are said to have the bivariate normal distribution.
The joint moment generating function for X and Y is .
(a) Find the marginal pdf
Lecture 10
Data Reduction
We should think about the following questions carefully before the
"simplification" process:
Is there any loss of information due to summarization?
How to compare the amount of information about in the
original data X and in ?
Lecture 11
1. (Regular) Exponential Family
The density function of a regular exponential family is:
Example. Poisson()
Example. Normal. (both unknown).
2. Theorem (Exponential family & sufficient
Statistic). Let be a random sample from the regular
exponen
Chapter 6. Interval Estimation
1.Introduction to the Pivotal Quantity Approach,
with an application in:
Deriving the Exact Confidence Interval for the
population mean when the population is normal
and the population variance is known.
Example. Let be a ra
Confidence Interval, continued
1. Sample size estimation based on the large sample
C.I. for p
From the interval p Z 2
(1
p p )
p (1 p )
, p + Z 2
n
n
L = lengh of your 100(1 )% CI = 2 Z 2
(1
p p)
n
L, , p are given and we are interested in sample si
AMS312
Quiz 6
Name: _ID:
_
This is a close book exam. Anyone who cheats will receive a grade of F for the entire course. Turn in by 12noon. (Use the front/back of this paper to finish your quiz.)
Suppose a random sample of size n is drawn from a normal po