Korea Advanced Institute of Science and Technology
Introduction to Probability and Statistics
MATH 208

Spring 2011
CC511: HW4
Due on Oct 18th, 2016
Problem 1:
The thickness of glass sheets produced by a certain process are normally distributed with
a mean of = 3.00 mm and a standard deviation of = 0.12 mm.
1. What is the probability that a glass sheet is thicker than
Korea Advanced Institute of Science and Technology
Introduction to Probability and Statistics
MATH 208

Spring 2011
CC511: HW5
Due on Nov 10th, 2016
Problem 1:
Let X1 , X2 , , Xn be a set of independent random variables with a U (0, ) distribution,
where > 0, and let
T = maxcfw_X1 , , Xn .
1. Express the likelihood function of in terms of T .
2. Find the maximum likel
Korea Advanced Institute of Science and Technology
Introduction to Probability and Statistics
MATH 208

Spring 2011
CC511: HW2
Due on Sept. 29th, 2016
Problem 1:
A random variable X takes values between 0 and with a cumulative distribution function
F (x) = A + Bex ,
for x > 0.
1. Find the values of A and B.
2. What is P (2 X 3)?
Solution.
1. F (0) = 0 A + B = 0
lim F
Korea Advanced Institute of Science and Technology
Introduction to Probability and Statistics
MATH 208

Spring 2011
CC511: HW 6
Due on Nov 22, 2016
Problem 1:
In an upaired twosample problem an experimenter observes n = 14, x = 32.45, sx = 4.30
from population A and m = 14, y = 41.45, sy = 5.23 from population B.
1. Use the pooled variance method to construct a 99% t
Korea Advanced Institute of Science and Technology
Introduction to Probability and Statistics
MATH 208

Spring 2011
CC511: HW1
Due on Sept. 20th, 2016
Problem 1: Use the three axioms only in the definition of probability (which is covered in
class), prove the followings:
1. P() = 0
2. A B = P(A) P(B)
3. P(Ac ) = 1 P(A)
Solution
1. 1 = P(S) = P(S ) = P(S) + P() = 1 + P
Korea Advanced Institute of Science and Technology
Introduction to Probability and Statistics
MATH 208

Spring 2011
CC511: HW3
Due on Oct 11th, 2016
Problem 1:
Consider the two independent random variables X1 B(n1 , p) and X2 B(n2 , p).
1. Use the Binomial theorem
n
X
n x nx
(p + q) =
p q
x
x=0
n
to show that
y
X
n1
n2
n1 + n2
=
.
x
yx
y
x=0
2. Prove that
P(X1 + X
Korea Advanced Institute of Science and Technology
Introduction to Probability and Statistics
MATH 208

Spring 2011
CC511: HW 8
Due on December 13, 2016
Problem 1:
Suppose that you have a random sample of (xi , yi ) of size n = 20. Suppose that the
following simple regression model is assumed
y i = 0 + 1 xi + e i ,
ei N (0, 2 )
and, from the regression analysis, you g
Korea Advanced Institute of Science and Technology
Introduction to Probability and Statistics
MATH 208

Spring 2011
CC511: HW 7
Due on December 6, 2016
Problem 1:
A balanced experimental design has k = 4 factor levels. The following table gives a
summary of outcomes for each levels.
Level (i)
Sample mean (
xi )
Sample variance (Si2 )
Sample size (ni )
1
7.05
70
10
2
7
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2015 Fall Semester Midterm
For General Chemistry I (CH101)
Date: October 21 (Wed),
Time Limit: 19:00 ~ 21:45
Student I.D. Number
Name
75 Normal Points + 8 Bonus Points
If you get 75 points out of 83 points, you will get the full 40% assigned to the midter
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2016 Fall Semester Midterm
For General Chemistry I (CH101)
Date: October 22 (Sat),
Time Limit: 19:00 ~ 22:00
Student I.D. Number
Name
90 Normal Points + 8 Bonus Points
If you get 90 points out of 98 points, you will get the full 40% assigned to the midter
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2015 SPRING Semester Midterm Examination
For General Chemistry I
Date: April 22 (Wed),
Time Limit: 19:00 ~ 21:00
Write down your information neatly in the space provided below; print your Student ID in the upper
right corner of every page.
Professor
Name
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2013 Fall Semester Midterm Examination
CH101 General Chemistry I
Date: October 23 (Wednesday), 2013
Time Limit: 7:00 ~ 9:00 p.m.
Write down your information neatly in the space provided below; print your Student ID in
the upper right corner of every page.
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2012 SPRING Semester Midterm Examination
For General Chemistry I
Date: March 28 (Wed),
Time Limit: 7:00 ~ 9:00 p.m.
Write down your information neatly in the space provided below; print your Student ID in the upper
right corner of every page.
Professor
Na
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2012 FALL Semester Midterm Examination
For General Chemistry I (CH101)
Date: October 24 (Wed),
Time Limit: 7:00 ~ 9:00 p.m.
Write down your information neatly in the space provided below; print your Student ID in the upper
right corner of every page.
Prof
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
CH101 General Chemistry Final Examination
Fall Semester 2014
Wednesday December 17
Time Limit: 19:00 ~ 21:00
Write down your answers neatly in the spaces provided below the questions; print your
Student ID in the upper righthand corner of every page.
Pro
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
CH101: General Chemistry I
MidTerm Examination
Fall Semester 2011
Tuesday 25 October. Time: 09.0011.30 (2.5 hours)
1. (a) Calculate the maximum wavelength of electromagnetic radiation that
can promote ejection of electrons from the surface of tungsten,
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
KAIST
Department of Mechanical Engineering
MAE 221 A/B/C 2016 Fall
ME 221 Fluid Mechanics Course Syllabus
Contact Information:
Section
Name
Email
Office (Phone)
A
Sung, Hyung Jin
[email protected]
N74,5114 (#3027)
B
Cho, Yeunwoo
[email protected]
N74
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2013 SPRING Semester Midterm Examination
For General Chemistry I
Date: April 24 (Wed),
Time Limit: 7:00 ~ 9:00 p.m.
Write down your information neatly in the space provided below; print your Student ID in the upper
right corner of every page.
Professor
Na
Korea Advanced Institute of Science and Technology
Calculus 1
MATH MAS101

Spring 2017
MAS 101 Calculus I : Final Exam
7:00 PM 10:00 PM
June 18, 2013
Spring 2013
MAS 101
Full Name :
Student Number:
Do not write in this box.
Instruction
No items other than pen, pencil, eraser and your id are allowed. You must leave all of your
belongings th
Korea Advanced Institute of Science and Technology
Calculus 1
MATH MAS101

Spring 2017
Calculus I
Final Exam Solution Criteria
2012 Spring
1 Find the interval of convergence of the power series.
1(a)
10 Points
X
2n (n!)2 n
x
(2n)!
n=0
Solution.
Ratio Test
(+2 point)
un+1
2 (n!) n
= lim 2(n + 1)(n + 1) x = 1 x
let un =
x . then lim
2
Korea Advanced Institute of Science and Technology
Calculus 1
MATH MAS101

Spring 2017
MAS 101 Calculus I : Final Exam
7:30 PM 10:30 PM
May 22, 2012
Spring 2012
MAS 101
Full Name :
Student Number:
Do not write in this box.
Instruction
No items other than pen, pencil, eraser and your id are allowed. You must leave all of your
belongings tha
Korea Advanced Institute of Science and Technology
Calculus 1
MATH MAS101

Spring 2017
Final Exam of Calculus I(MAS101)
2010. 5. 18(Tue)
7:00 PM 10:00 PM
Spring 2010
MAS101
Full Name :
Student Number:
Seat Number :
Do not write in this box.
Directions
Turn o your mobile phone. No items other than pen, pencil, eraser and your id are allowed
Korea Advanced Institute of Science and Technology
Calculus 1
MATH MAS101

Spring 2017
MAS 101 Calculus I : Final Exam
7:00 PM 10:00 PM
June 17, 2014
Spring 2014
MAS 101
Full Name:
Student Number:
Class Section:
Do not write in this box.
Instruction
No items other than pen, pencil, eraser and your id are allowed. You must leave all of
your
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2016 Fall MAS101 Calculus 1
Homework 5
Due: October 7, 2016
5.1. Determine all values of p for which the integral converges and evaluate the integral for
those values of p.
Z
1
dx.
(a)
x(ln x)p
e
Z e
1
(b)
dx.
p
1 x(ln x)
Z 1
(c)
xp ln x dx.
0
Z
b
x
dx =
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2016 Fall MAS101 Calculus 1
Homework 2
Due: Sep. 22 11:59PM, 2016
2.1. Find an equation of the curve that passes through the point (0, 1) and whose slope at
x
(x, y) is xey .
2.2. Solve the following differential equations. (Write y as a function of x.)
(
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2016 Fall MAS101 Calculus 1
Homework 10
Due: November 25, 2016
10.1. (a) Draw the graph of the curve described by the following polar equation and find
its length.
2
r = cos
2
(b) Draw the graph of the curve described by the following polar equation and
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2016 Fall MAS101 Calculus 1
Homework 13
Due: Practice Only. Do not submit
13.1. Find a parametric equation for the line of intersection of the following planes in R3 .
z = x + y,
2x 5y z = 1.
13.2. Show that the lines x = y = z and x + 1 =
between these l
Korea Advanced Institute of Science and Technology
MATH 101

Spring 2011
2016 Fall MAS101 Calculus 1
Homework 3
Due: September 30, 2016
3.1. Calculate the follwing.
(a)
Z
x4 ln x dx
(b)
1
Z
tan1 x dx.
0
(c)
Z
ex cos2 x dx
3.2. Calculate the follwing.
(a)
Z
x sin x sec2 x dx
(b)
Z
x
dx
9x2 + 3x
(c)
Z
x2
dx
4 x2
3.3. (a) Show th