UCSD ECE 153
Prof. Young-Han Kim
Handout #6
Thursday, October 9, 2008
Solutions to Homework Set #1
(Prepared by TA Halyun Jeong)
1. Read Sections 2.1 to 2.5 in the text. Try to work on all examples.
2. World Series. The World Series is a seven-game series
UCSD ECE 153 Prof. Young-Han Kim
Handout #18 Thursday, November 6, 2008
Homework Set #5 Due: Thursday, November 20, 2008
1. Work on the midterm problems to make sure you understand everything clearly. 2. Read Sections 6.16.5 in the text. Try to work on al
EE 278
Statistical Signal Processing
Handout #18
Friday, Aug. 14, 2009
Final Exam
This is a three hour exam. The total number of points is 100.
The exam is open book and open notes. Hoewever, computer/internet use is not
permitted.
You can quote any res
EE 178
Probabilistic Systems Analysis
Tuesday, March 10, 2009
Handout #22
Sample Final Problems
The following are old exam problems. To prepare for the nal you will also need to review
the lecture notes, the homework, midterm review, and midterm problems.
EE 278
Statistical Signal Processing
Handout #19
Friday, August 14, 2009
Final Exam Solutions
1. (13 points)
(a) (9 points) We will rst calculate the following expectations that will be used in
our calculations later on.
E (X 2 ) = 1;
E (XY1 ) = E (X 2 )
EE 178
Probabilistic Systems Analysis
Wednesday, March 18, 2009
Handout #24
Sample Final Solution
1. a. . This follows by the union-of-events bound:
100
P(100 Ai )
i=1
P(Ai ) 102
i=1
max P(Ai )
1i100
0.01.
b. . For each Z = z ,
Var(X + Y |Z = z ) = Var(X
EE 178
Probabilistic Systems Analysis
Handout #14
Thursday, February 19, 2009
Homework #6
Due Thursday, February 26
1. Uncorrelation vs. Independence.
Let X and Y be random variables with joint pdf
fX,Y (x, y ) =
c if 0 |x| |y |, 0 |y | 1
0 otherwise,
whe
EE 178
Probabilistic Systems Analysis
Handout #18
Tuesday, March 3, 2009
Homework #6 Solutions
1. (15 points)
a. To nd c we inspect the region R where the pdf fX,Y (x, y ) is nonzero, as shown in
Figure 1. The area of this region is 2the area of the two t
EE 178
Probabilistic Systems Analysis
Sunday, February 7, 2009
Handout #10
Sample Midterm Problem Solutions
1. a. (). Consider
P(A) = P(A|C )P(C ) + P(A|C c )P(C c )
P(B |C )P(C ) + P(B |C c )P(C c )
= P(B ).
b. (=). Consider
P(n=1 Ai ) = P(n=1 Ac )c ),
EE 278
Statistical Signal Processing
Handout #10
Wednesday, July 22, 2009
Midterm
This is a 1 hour and 45 minute exam. The exam is open everything except for laptop
and internet connection. The total number of points is 80. Please begin each problem
solut
EE 178
Probabilistic Systems Analysis
Thursday, February 12, 2009
Handout #13
Midterm Solution
1. a. (=). Consider
1 P(Ac B ) = P(Ac B )c )
= P(A B c ) by DeMorgan
= P(A) P(A B ).
b. (). Since P(A|B ) = P(B |A),
P(A, B )
P(A, B )
=
.
P(B )
P(A)
Thus, P(A)
EE 278 Statistical Signal Processing Midterm Solution
Handout #11 Monday, July 27, 2009
1. (a) . P (A) = P (A|B)P (B)+P (A|B c )P (B c ) mincfw_P (A|B), P (A|B c )(P (B)+P (B c ) = mincfw_P (A|B), P (A|B c ). (b) . FXY (x, y) = P (X x, Y y) P (X x) = FX (
EE 278 Statistical Signal Processing Sample Midterm This is a sample midterm. 1. (20 points) Inequalities.
Saturday, July 18, 2009 Handout #8
Label each of the following statements with =, , , or None. Label a statement with = if equality always holds. La
UCSD ECE 153 Prof. Young-Han Kim
Handout #7 Thursday, October 9, 2008
Homework Set #2 Due: Thursday, October 16, 2008
1. Read Sections 3.13.2, 3.43.6, 4.14.2, 4.44.5, 4.7, 4.9, 5.1-5.5, 5.7-5.8 in the text. Try to work on all examples.
2. Jurors fallacy.
UCSD ECE 153 Prof. Young-Han Kim
Handout #9 Thursday, October 16, 2008
Homework Set #3 Due: Thursday, October 24, 2008
1. Read Sections 6.5.1, 8.6.18.6.2 in the text. Try to work on all examples. 2. Coin with random bias. You are given a coin but are not
UCSD ECE 153 Prof. Young-Han Kim
Handout #10 Thursday, October 23, 2008
Solutions to Homework Set #3 (Prepared by TA Halyun Jeong)
1. Read Sections 6.5.1, 8.6.18.6.2 in the text. Try to work on all examples. 2. Coin with random bias. You are given a coin
UCSD ECE 153 Prof. Young-Han Kim
Handout #11 Thursday, October 23, 2008
Homework Set #4 Due: Thursday, October 30, 2008
1. Read Sections 4.3, 4.6, 5.7, 5.9, 6.5 in the text. Try to work on all examples. 2. Two envelopes. An amount A is placed in one envel
UCSD ECE 153 Prof. Young-Han Kim
Handout #16 Thursday, October 30, 2008
Solutions to Homework Set #4 (Prepared by TA Halyun Jeong)
1. Read Sections 4.3, 4.6, 5.7, 5.9, 6.5 in the text. Try to work on all examples. 2. Two envelopes. An amount A is placed i
UCSD ECE 153 Prof. Young-Han Kim
Handout #20 Thursday, November 20, 2008
Homework Set #6 Due: Thursday, December 4, 2008
1. Read Sections 7.17.4, 9.19.6, 10.110.2, 10.4 in the text. Try to work on all examples. 2. Symmetric random walk. Let Xn be a random
UCSD ECE 153 Prof. Young-Han Kim
Handout #24 Thursday, December 4, 2008
Solutions to Homework Set #6 (Prepared by TA Halyun Jeong)
1. Read Sections 7.17.4, 9.19.6, 10.110.2, 10.4 in the text. Try to work on all examples. 2. Symmetric random walk. Let Xn b
Lecture Notes 8
Random Processes
EE278
Prof. B. Prabhakar
Statistical Signal Processing
Autumn 02-03
Denition and simple examples
Discrete Time Random Processes
IID
Random Walk Process
Mean and Autocorrelation Function
Gaussian Random Processes
Copy
Example: Oscillator with Random Phase
Consider the output of a sinusoidal oscillator that has a random phase and amplitude of the form: X(t) = cos (c t + ) , where U([0, 2]). Writing out the explicit dependence on the underlying sample space S the oscilla
UCSD ECE 153
Prof. Young-Han Kim
Handout #8
Thursday, October 16, 2008
Solutions to Homework Set #2
(Prepared by TA Halyun Jeong)
1. Read Sections 3.13.2, 3.43.6, 4.14.2, 4.44.5, 4.7, 4.9, 5.1-5.5, 5.7-5.8 in the text. Try to
work on all examples.
2. Juro
UCSD ECE 153
Prof. Young-Han Kim
Handout #19
Thursday, November 20, 2008
Solutions to Homework Set #5
(Prepared by TA Halyun Jeong)
1. Work on the midterm problems to make sure you understand everything clearly.
2. Read Sections 6.16.5 in the text. Try to
EE 278 Statistical Signal Processing Sample Midterm Solutions 1. (20 points) Inequalities. a. (2 points) None. Since P(A|B) = P(B|A)P(A) P (B)
Saturday, July 18, 2009 Handout #9
and P(A) can be larger or less than P(B), no equality or inequality holds in