King Abdullah University of Science and Technology
Probability and random process
AMCS 241

Spring 2016
AMCS 241: Midterm Exam Solutions
1. We have
Z
fX (z x)fY (x) dx.
fZ (z) = (fX fY )(z) =
Note that
(
e(zx)
fX (z x) =
0
xz
.
x>z
Therefore,
Z
z
fZ (z) =
e(zx) fY (x) dx =
(R z
0
e(zx) ex dx
0
z0
.
z<0
Note that
Z
0
z
(
2 zez
Rz
e(zx) ex dx =
ez 0 e()x dx
=
King Abdullah University of Science and Technology
Probability and random process
AMCS 241

Spring 2016
AMCS 241: Homework 3
Assigned: Sunday Feb. 12
Due: Sundary Feb. 19 in class (by 9:00am)
Instructions: Follow the guidelines for homework writeups in the syllabus. If the TAs cannot understand /
read your solution, then you will not receive credit. You ar
King Abdullah University of Science and Technology
Probability and random process
AMCS 241

Spring 2016
AMCS 241: Homework 1
Assigned: Sun Jan. 29
Due: Sun Feb. 5 (by 6:00pm in my office or in class)
Instructions: Follow the guidelines for homework writeups in the syllabus. If the TAs cannot understand /
read your solution, then you will not receive credit
King Abdullah University of Science and Technology
Probability and random process
AMCS 241

Spring 2016
AMCS 241: Homework 2
Assigned: Sunday Feb. 5
Due: Sunday Feb. 12 in class (by 9:00am)
Instructions: Follow the guidelines for homework writeups in the syllabus. If the TAs cannot understand /
read your solution, then you will not receive credit. You are
King Abdullah University of Science and Technology
Probability and random process
AMCS 241

Spring 2016
AMCS 241: Homework 4
Assigned: Tuesday Feb. 21
Due: Tuesday Feb. 28 in class (by 9:00am)
Instructions: Follow the guidelines for homework writeups in the syllabus. If the TAs cannot understand /
read your solution, then you will not receive credit. You a
King Abdullah University of Science and Technology
Probability and random process
AMCS 241

Spring 2016
AMCS 241: Homework 6
Assigned: Tuesday Mar. 21
Due: Tuesday Mar. 28 in class (by 9:00am)
Instructions: Follow the guidelines for homework writeups in the syllabus. If the TAs cannot understand /
read your solution, then you will not receive credit. You a
King Abdullah University of Science and Technology
Probability and random process
AMCS 241

Spring 2016
AMCS 241: Homework 5
Assigned: Tuesday Feb. 28
Due: Tuesday Mar. 7 in class (by 9:00am)
Instructions: Follow the guidelines for homework writeups in the syllabus. If the TAs cannot understand /
read your solution, then you will not receive credit. You ar
King Abdullah University of Science and Technology
CALCULES
AMCS 101

Spring 2015
1
1.1
1.2
1.3
1.4
1.5
2
1.1
3
()
() ()
Si
GaAs
ZnO
MoS2
Ge
InP
SiC
WS2
GaP
GaN
MoSe2
AlAs
InN
WSe2
AlP
SixGe1xAlxGa1xAsInxGa1xN
GaAsxP1x ZnxMg1xO InxGa1xAsyP1y GaxIn1xNy1Asy2Sb1y1y2
4
5
Si
SiWafer
Si18
6
SiC
GaN
6
King Abdullah University of Science and Technology
CALCULES
AMCS 101

Spring 2015
1
2.1
2.2
2.3
2.4
2
2.1
2.1.1
(1)
The word atom was initially coined by ancient Greek philosophers,
.
In the early 1800s, John Dalton used the concept of atoms to explain
why elements always react in ratios of small whole numbers (the law of
King Abdullah University of Science and Technology
Linear Algebra
AMCS 102

Fall 2015
Cartesian components
of vectors
Any vector may be expressed in Cartesian components, by using unit vectors in the directions
of the coordinate axes. In this unit we describe these unit vectors in two dimensions and in
three dimensions, and show how they c
King Abdullah University of Science and Technology
CALCULES
AMCS 101

Spring 2015
Some guidelines and recommendations regarding the Homework Problem sets:
1. Each problem is worth 1%.
2. You have to solve your homework problems on your own.
3. When working out the solutions, you are encouraged (but not required) to use technical co
King Abdullah University of Science and Technology
Introduction to Probability and Statistics
AMCS 143

Fall 2015
1
KAUST
AMCS 143 Introduction to Probability and Statistics
(Fall 15)
Review Session Exam 2
Date: Tue Oct. 27 , 2015.
Problem 1:
The measurements of the distance to a certain object is accomplished by symmetric and random
errors. The symmetric errors equa
King Abdullah University of Science and Technology
Introduction to Probability and Statistics
AMCS 143

Fall 2015
1
KAUST
AMCS 143 Introduction to Probability and Statistics
(Fall15)
Recitation 8
Pairs of Continuous RVs: bivariate PDF, CDF, Conditional Distribution
Date: Tue Oct. 27, 2015.
Problem 1:
2
Problem 2:
Problem 3:
Problem 4:
King Abdullah University of Science and Technology
Introduction to Probability and Statistics
AMCS 143

Fall 2015
1
KAUST
AMCS 143 Introduction to Probability and Statistics
(Fall15)
Tutorial 8
Pairs of Continuous RVs: bivariate PDF, CDF, Conditional Distribution
Date: Tue Oct. 27, 2015.
Problem 1:
2
Problem 2:
Problem 3:
Problem 4: