UCSD ECE 153
Prof. Young-Han Kim
Handout #14
Thursday, April 21, 2011
Solutions to Homework Set #3
(Prepared by TA Yu Xiang)
1. Time until the n-th arrival. Let the random variable N (t) be the number of packets arriving
during time (0, t]. Suppose N (t)
UCSD ECE153
Prof. Young-Han Kim
Handout #24
Tuesday, May 3, 2011
Solutions to Midterm Examination (Spring 2010)
(Prepared by TA Lele Wang)
1. Let Xi denote the color of the i-th ball.
(a) By symmetry, Pcfw_X1 = R = 1/2.
(b) Again by symmetry, Pcfw_Xi = R
UCSD ECE153
Prof. Young-Han Kim
Handout #23
Tuesday, May 3, 2011
Solutions to Midterm (Spring 2008)
1. First available teller (20 points). Consider a bank with two tellers. The service times for
the tellers are independent exponentially distributed random
UCSD ECE153
Prof. Young-Han Kim
Handout #22
Tuesday, May 3, 2011
Solutions to Midterm (Fall 2008)
1. Coin with random bias.
Let P be a random variable distributed uniformly over [0, 1]. A coin with (random) bias P is
ipped three times. Assume that the val
UCSD ECE153
Prof. Young-Han Kim
Handout #40
Thursday, June 2, 2011
Solutions to Final (Spring 2010)
1. Polyas urn revisited (40 points).
Suppose we have an urn containing one red ball and one blue ball. We draw a ball at random
from the urn. If it is red,
UCSD ECE153
Prof. Young-Han Kim
Handout #39
Thursday, June 2, 2011
Solutions to Final (Spring 2008)
1. Coin with random bias (20 points). You are given a coin but are not told what its bias
(probability of heads) is. You are told instead that the bias is
UCSD ECE153
Prof. Young-Han Kim
Handout #38
Thursday, June 2, 2011
Solutions to Final (Fall 2008)
1. Order statistics. Let X1 , X2 , X3 be independent and uniformly drawn from the interval [0, 1].
Let Y1 be the smallest of X1 , X2 , X3 , let Y2 be the med
UCSD ECE153
Prof. Young-Han Kim
Handout #27
Tuesday, May 10, 2011
Solutions to Midterm
(Total: 100 points)
There are 3 problems, each problem with multiple parts, each part worth 10 points. Your
answer should be as clear and readable as possible.
1. Lotte
UCSD ECE153
Prof. Young-Han Kim
Handout #26
Tuesday, May 10, 2011
Midterm Examination
(Total: 100 points)
There are 3 problems, each problem with multiple parts, each part worth 10 points. Your
answer should be as clear and readable as possible.
1. Lotter
UCSD ECE153
Prof. Young-Han Kim
Handout #3
Tuesday, March 29, 2011
Information Sheet
Name:
Major:
Year:
ECE 109:
1,
2,
Yes,
3,
4,
No.
Reasons for taking this course:
Random remarks:
5+,
MS,
PhD
If yes, when and which textbook?
UCSD ECE 153
Prof. Young-Han Kim
Handout #41
Thursday, June 2, 2011
Solutions to Homework Set #7
(Prepared by TA Yu Xiang)
1. Symmetric random walk. Let Xn be a random walk dened by
X0 = 0,
n
Xn =
Zi ,
i=1
1
where Z1 , Z2 , . . . are i.i.d. with Pcfw_Z1 =
UCSD ECE153
Prof. Young-Han Kim
Handout #32
Thursday, May 26, 2011
Solutions to Homework Set #6
(Prepared by TA Lele Wang)
1. Covariance matrices. Which of the following matrices can be a covariance matrix? Justify
your answer either by constructing a ran
UCSD ECE153
Prof. Young-Han Kim
Handout #25
Thursday, May 5, 2011
Solutions to Homework Set #5
(Prepared by TA Lele Wang)
1. Neural net. Let Y = X + Z , where the signal X U[1, 1] and noise Z N (0, 1) are
independent.
(a) Find the function g (y ) that min
UCSD ECE153
Prof. Young-Han Kim
Handout #17
Thursday, April 28, 2011
Solutions to Homework Set #4
(Prepared by TA Lele Wang)
1. Two independent uniform random variables.
Let X and Y be independently and uniformly drawn from the interval [0, 1].
(a) Find t
UCSD ECE 153
Prof. Young-Han Kim
Handout #11
Thursday, April 14, 2011
Solutions to Homework Set #2
(Prepared by TA Lele Wang)
1. Polyas urn. Suppose we have an urn containing one red ball and one blue ball. We draw a
ball at random from the urn. If it is
UCSD ECE153
Prof. Young-Han Kim
Handout #8
Thursday, April 7, 2011
Solutions to Homework Set #1
(Prepared by TA Yu Xiang)
1. World Series. The World Series is a seven-game series that terminates as soon as either
team wins four games. Suppose San Diego Pa
UCSD ECE153
Prof. Young-Han Kim
Handout #5
Tuesday, March 29, 2011
Solutions to ECE153 Aptitude Test
rn =
1.
n=0
1
.
1r
Solution: Let
S = 1 + r + r2 + .
(The series converges since 0 < r < 1.) Then
rS = r + r2 + r3 + .
Taking the dierence between two equa
UCSD ECE153
Prof. Young-Han Kim
Handout #4
Tuesday, March 29, 2011
ECE153 Aptitude Test
Name (Optional):
Simplify the following equations as much as you can. Throughout r (0, 1).
rn =
1.
n=0
nrn =
2.
n=0
3.
n=0
rn
=
n!
1
n
nk
r (1 r)nk =
k
4.
k=0
n
5.
k
k