Korea Advanced Institute of Science and Technology
Intro to Linear Algebra
MAS 109

Fall 2016
2016 Fall MAS109 Homework 1 Solution
Problem 1. Determine whether the vector u = (1, 5, 3) can be expressed as a linear
combination of the vectors v1 = (1, 2, 3), v2 = (1, 3, 5), v3 = (2, 3, 1). If it is possible,
find such a linear combination.
Solution.
Korea Advanced Institute of Science and Technology
investments
MAS 250

Spring 2017
Stock Valuation
KAIST Graduate School of Finance and
Accounting
Jangkoo Kang
Readings
Chapter 5: Introduction to risk, return, and the historical record, in
Bodie, Kane, Marcus, and Jain, 2013, Investments, McGrawHill
Irwin.
Chapter 18: Equity valuation
Korea Advanced Institute of Science and Technology
investments
MAS 250

Spring 2017
FE 502 Statistical Analysis for Finance (SpringI 2017)
7 Properties of Point Estimators
Example 7.1
X i 1 X i n is an estimator of .
n
S 2 i 1 ( X i X ) 2 (n 1) is an estimator of 2 .
n
Why do we prefer X (or S 2 ) to other estimators of (or 2 )? Becau
Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
FE 502 Statistical Analysis for Finance (SpringI 2017)
10 Statistical Inference with Two populations:
Tests for the Equality of Two Means and Proportions
10.1 Summary: Two IND normally distributed samples
12 , 22 are known
12 , 22 are unknown
( N (0,1) d
Korea Advanced Institute of Science and Technology
investments
MAS 250

Spring 2017
Ch 3 Hedging Strategies
Using Futures
Byun, Suk Joon
KAIST Business School
Hedging
100 gallons
?
FE505 Derivatives
2
KAIST Business School
Basis Risk
Basis = Spot price of asset to be hedged
(fuel spot price)
Futures price of contract use
Korea Advanced Institute of Science and Technology
investments
MAS 250

Spring 2017
FE 502 Statistical Analysis for Finance (SpringI 2017)
8 Confidence Intervals ()
(Interval Estimation)
8.1 Summary
Summary
For any symmetric distribution of , 100(1 ) % confidence interval for is given by
(1) Z 2 se()
if 2 is known ( Z ~ N (0,1) distribu
Korea Advanced Institute of Science and Technology
investments
MAS 250

Spring 2017
FE 502 Statistical Analysis for Finance (SpringI 2017)
9 Hypothesis Testing ()
1. Confidence interval approach  statisticians point of view
2. Critical value approach  Gods point of view
2. pvalue approach
9.1 Hypothesis Testing using Confidence inter
Korea Advanced Institute of Science and Technology
investments
MAS 250

Spring 2017
Consumption/Investment Decisions under Certainty
KAIST Graduate School of Finance and
Accounting
Jangkoo Kang
Robinson Crusoe Economy
Suppose that Robinson Crusoe is endowed with E of wheat
(consumption goods), which can be consumed this year (t0) or be
s
Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
MAS250(B) Quiz #2
2016.09.26
Student ID:
Name:
1. There are three coins C1 , C2 , C3 in an urn and their probabilities of heads are 1/4, 1/2,
3/4 respectively. One coin is chosen from the urn (uniformly) and that coin is tossed twice.
Given that the two t
Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
MAS250(B) Quiz #3
2016.10.10
Student ID:
Name:
1. Suppose that X has density function
ax if 0 < x < 1
f (x) =
0
otherwise.
Find the constant a. Also, find limn nE[X n ]
[Solution]
Z
x
a = 2 and thus, F (x) =
2tdt = x2
0
FX n (x) = P (X x1/n ) = x2/n
2 2/n
Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
MAS250 Ch.04 Solutions
(7, 13, 16, 20, 26, 29, 30, 36, 39, 42, 49, 53, 54, 56, 57)
7. The probability that a given radio tube will last less than 150 hours is
Z 150
100
1
dx = .
2
x
3
50
Therefore, the desired probability is
5 1 2
1
80
( ) (1 )3 =
.
2 3
Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
MAS250 Ch.03 Solutions
(6, 7, 13, 14, 22, 30, 33, 41, 48)
6. (a) EF c Gc
(f) E c F c Gc
(b) EF c G
(c) E F G
(g) E c F c E c Gc F c Gc
(i) EF Gc EF c G E c F G
7. (a) S
(b) 0
(d) EF EG F G
(c) E
(e) EF G
(h) (EF G)c
(j) S
(d) EF
(e) F EG
13. (a) Since E =
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2014
SYLLABUS
Course Type
Elective
Course Code
EE304
Course Name
Korean
Course Name
English
Electronic Circuits
Name
Lecture:Exp.:Credit(Homework)
3:0:3
Mutually Recognized Course(BS/MS) : ( O )
Term : Spring, Fall
This course is devised to teach electronic ci
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2014
SYLLABUS
Course Type
Elective
Course Code
EE474
Course Name
Korean
Course Name
English
Introduction to Multimedia
Name
Lecture:Exp.:Credit(Homework)
3:0:3(6)
Mutually Recognized Course (Undergraduate/Graduate): (O )
Descriptions
of Courses
Term : Spring
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2014
SYLLABUS
Course Type
Elective
Course Code
EE323
Course Name
Korean
Course Name
English
Computer Networks
Name
Lecture:Exp.:Credit(Homework)
3:0:3
Mutually Recognized Course(BS/MS) : ( X )
Descriptions
of Courses
Term : Spring
The Internet is profoundly
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2014
(Note to the student: This is a syllabus from the last time the course was offered. A
new syllabus will be distributed during the class. The content will be similar but not
necessarily identical.)
Environmentalism: A Historical Survey
Spring 2015
Tuesdays
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2014
MAS201 Differential Equations and Applications
2015 Spring Semester
Class
A
B
C
D
Tu,
Tu,
Mo,
Mo,
Lecture hours
Th 10:30AM11:45AM
Th 09:00AM10:15AM
We 13:00PM14:15PM
We 09:00AM10:15AM
Lecture room
E11410
E11?
E11?
E11?
Lecturer
Kwon, Kil Hyun
Ref.
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2014
MAS201 Differential Equations and Applications
2015 Spring Semester
Class
A
B
C
D
Tu,
Tu,
Mo,
Mo,
Lecture hours
Th 10:30AM11:45AM
Th 09:00AM10:15AM
We 13:00PM14:15PM
We 09:00AM10:15AM
Lecture room
E11410
E11?
E11?
E11?
Lecturer
Kwon, Kil Hyun
Ref.
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2014
*MAS201 Differential Equations and Applications_2014 Spring_v.1*
MAS201A[LEETu,TH9:00]
MAS201B[CHOITu,TH13:00]
MAS201C[TOMOOM,W13:00]
MAS201D[SCHWEIZERM,W10:30]
1.
Course Outline: This course introduces the basics of differential equations. The to
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2013
Homework #12 (due 12/7)
[9.7]
[9.8]
[9.9] # 19, 24
#
3,
#
9,
16,
22,
18
34
#E1: Draw all the spanning trees of K2,2 and indicate the isomorphism classes of these.
How many isomorphism classes are there?
#E2: How many graphs have n vertices labeled v1, v2,
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2013
Homework #10 (due 11/23)
[8.5] # 21, 28
[8.6] # 23, 24, 25, 28
[8.7] # 7, 8, 18, 19, 20
[Extra problem]
A coloring of a simple graph is the assignment of a color
to each vertex of the graph so that no two adjacent vertices
are assigned the color. This can
Korea Advanced Institute of Science and Technology
MAS 223

Spring 2013
Homework #9 (due Nov 16)
[Exercise Problems from the textbook : 90 pts]
[8.1]
[8.2]
[8.3]
[8.4]
41, 42 (prove your answer).
42, 46, 47
29, 32
10, 11
[Extra Problem: 10 pts]
The tail recursion is referred to a special case of recursion
where the last opera