Math230 Probability and Statistics . 2015-06-18
Final Examination 19:00 22:00
You may write answers either in English or Korean. -
1. [10] Let X1, . . . , Xn be a random sample from a distribution with mean a and variance 0'2. Denote
n
_ 1 1 _
the sample
Math230 Probability and Statistics 2014-0619
Final Examination 19:00 22:00
- You may write answers either in English or Korean. v
1. [20] Let X1 and X2 be independent Poisson random variables with densities
for j = 1, 2, respectively.
(a) [10] Find the
MidTermExamMATH230:EI~ 2-! %7ll October 24th, 2015
(1) (5 pts.) Prove that if the events 31,32,- -~Bk constitute a partition of the
sample space S such that P(Bi) 75 0 for z' = 1, 2, - - , k, then for any event A
in S such that P(A) 0,
P(B, n A) P(B,)P(
Math230 Probability and Statistics 2015-0423 (Thu)
Midterm Examination 19:00 22:00
1.
2.
3.
the other has the probability q = 1 p of turning up head.
4.
O1
You may write answers either in English or Korean.
[10] Verify that for any events A, B,
max(P(A)
()
April 25, 2013
* . .
* .
1. (10pts) Suppose that POSTECH students from departments of P , Q, R are taking
MATH230. The students from departments of P , Q, R get A grades in MATH230
with probabilities p, q and r respectively. When a student got an A, w
Final Exam (Math 230: Probability and Statistics) Spring 2012
This ekam consists of 10 problems. Out of these 10, choose 8 problems and only these
8 problems will count for your grade. On your exam sheet you, should write which prob
lems, you want to be g
Math230 Probability and Statistics
Midterm Examination
2014-04-24
19:00 22:00
1. [10] Let P (A) = a and P (B) = b. Verify that
max(a, b) P (A B) min(a + b, 1),
and indicate when the equalities hold.
(Sol)
(i) Since A A B, we have P (A) P (A B). Likewise,
Mid Term Exam (Math 230: Probability and Statistics) Spring 2012
This exam consist of 7 problems with a total of 100 points.
1 (10 points) Suppose that B and B constitute a partition of the sample space S with
P(B) : 0.4. Let A be an event with P(A) > 0 s
()
April 25, 2013
* . .
* .
1. (10pts) Suppose that POSTECH students from departments of P , Q, R are taking
MATH230. The students from departments of P , Q, R get A grades in MATH230
with probabilities p, q and r respectively. When a student got an A, w
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter
design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Mathematical expression of reconstruction
Reconstructed signal becomes
Is this the same as
?
2
Matlab programming and homework
clf;
Ts=1/14;f=7;
%Ts should be smaller than
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Class information
Lecturer information
Name: Junil Choi ( )
Email: [email protected]
Office: LG 401
Office hours: Monday/Tuesday 3:30pm-4:30pm
TA information
Name: Se
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Class information
Lecturer information
Name: Junil Choi ()
Email: [email protected]
Office: LG 401 (LG 305 until 9/6)
(Temporal ) Office hours: Tuesday/Thursday 3:30pm-4:3
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter
design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Class information
Lecturer information
Name: Junil Choi ()
Email: [email protected]
Office: LG 401
Office hours: Monday/Tuesday 3:30pm-4:30pm (Only today, 5:00pm-6:00pm)
T
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Announcement
No classes on 9/13 (Tuesday), 9/20 (Tuesday), 9/22 (Thursday)
Will have backup classes for all cancelled classes later
2
Course at glance
Discrete-time
signals
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Homework
Due 12/13 (Tuesday) by the beginning of class (will accept until 2:10pm)
Problems in textbook: 6.24, 6.25, 6.32
2
Course at glance
Discrete-time
signals and systems
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Discrete-time sequences
Unit sample sequence (impulse)
Unit step sequence
Exponential/sinusoidal sequences and their periods
Discrete-time systems
Memoryless systems
Line
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct
DFT (FFT) Applications
1
DFT applications
Short list from Wikipedia
Spectral analysis
Filter bank
Data compression
Partial differential equations
Multiplication of large integers
Convolution
.
We will briefly discuss spectral analysis and digital subbandi
Digital Signal Processing
POSTECH
Department of Electrical Engineering
Junil Choi
Course at glance
Discrete-time
signals and systems
Discrete-time signals
Fourier-domain
representation
Sampling and
reconstruction
Discrete-time systems
Filter design
Struct