UCSD ECE 153
Prof. Young-Han Kim
Handout #20
Thursday, April 24, 2014
Solutions to Homework Set #3
(Prepared by TA Fatemeh Arbabjolfaei)
1. Time until the n-th arrival. Let the random variable N (t) be the number of packets arriving
during time (0, t]. Su
Solutions to Homework Set #3
(Prepared by 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) is Poisson with pmf
(t)n t
e
for n = 0, 1, 2, . . . .
n!
Let the random v
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
is
sh
Th
https:/www.coursehero.com/file/5662409/ece-153-hw3/
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
is
sh
Th
https:/www.coursehero.com/file/5662409/ece-153-hw3/
ar stu
ed d
vi y
UCSD ECE153
Prof. Young-Han Kim
Handout #13
Thursday, April 17, 2014
Homework Set #3
Due: Thursday, April 24, 2014
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) is Poisson
UCSD ECE 153
Prof. Young-Han Kim
Handout #11
Thursday, April 14, 2011
Solutions to Homework Set #2
(Prepared by 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 red
UCSD ECE153
Prof. Young-Han Kim
Handout #33
Thursday, May 26, 2011
Homework Set #7
Due: Thursday, June 2, 2011
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 = 1 = Pcfw_Z
UCSD ECE153
Prof. Young-Han Kim
Handout #26
Thursday, May 19, 2011
Homework Set #6
Due: Thursday, May 26, 2011
1. Covariance matrices. Which of the following matrices can be a covariance matrix?
Justify your answer either by constructing a random vector X
UCSD ECE 153
Prof. Young-Han Kim
Handout #12
Thursday, April 17, 2014
Solutions to Homework Set #2
(Prepared by TA Fatemeh Arbabjolfaei)
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
UCSD ECE153
Prof. Young-Han Kim
Handout #19
Thursday, April 24, 2014
Homework Set #4
Due: Thursday, May 1, 2014
1. Two envelopes. An amount A is placed in one envelope and the amount 2A is placed
in another envelope. The amount A is xed but unknown to you
UCSD ECE153
Prof. Young-Han Kim
Handout #21
Thursday, May 1, 2014
Homework Set #5
Due: Tuesday, May 6, 2014
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 minimizes
MSE = E (s
UCSD ECE153
Prof. Young-Han Kim
Handout #8
Wednesday, April 9, 2014
Homework Set #2
Due: Thursday, April 17, 2014
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 red, we put
UCSD ECE153
Prof. Young-Han Kim
Handout #23
Thursday, May 1, 2014
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 rando
UCSD ECE153
Prof. Young-Han Kim
Handout #7
Wednesday, April 2, 2014
Homework Set #1
Due: Wednesday, April 9, 2014
1. World Series. The World Series is a seven-game series that terminates as soon as
either team wins four games and is won mostly by the Unit
UCSD ECE153
Prof. Young-Han Kim
Handout #27
Tuesday, May 6, 2014
Solutions to Homework Set #5
(Prepared by TA Fatemeh Arbabjolfaei)
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) t
UCSD ECE153
Prof. Young-Han Kim
Handout #10
Thursday, April 10, 2014
Solutions to Homework Set #1
(Prepared by TA Fatemeh Arbabjolfaei)
1. World Series. The World Series is a seven-game series that terminates as soon as either
team wins four games. Suppos
UCSD ECE153
Prof. Young-Han Kim
Handout #34
Tuesday, May 27, 2014
Solutions to Homework Set #6
(Prepared by TA Fatemeh Arbabjolfaei)
1. Linear estimator. Consider a channel with the observation Y = XZ, where the signal X and
2 = 5,
the noise Z are uncorre
UCSD ECE153
Prof. Young-Han Kim
Handout #33
Thursday, May 22, 2014
Homework Set #7
Due: Thursday, May 29, 2014
1. Spaghetti. We have a bowl with n spaghetti strands. You randomly pick two strand
ends and join them. The process is continued until there are
UCSD ECE 153
Prof. Young-Han Kim
Handout #41
Thursday, May 29, 2014
Solutions to Homework Set #7
(Prepared by TA Fatemeh Arbabjolfaei)
1. Spaghetti. We have a bowl with n spaghetti strands. You randomly pick two strand ends and
join them. The process is c
UCSD ECE 153
Prof. Young-Han Kim
Handout #46
Thursday, June 5, 2014
Solutions to Homework Set #8
(Prepared by TA Fatemeh Arbabjolfaei)
1. Discrete-time Wiener process. Let Zn , n 0 be a discrete time white Gaussian noise (WGN)
process, i.e., Z1 , Z2 , . .
UCSD ECE153
Prof. Young-Han Kim
Handout #8
Wednesday, April 9, 2014
Homework Set #2
Due: Thursday, April 17, 2014
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 red, we put
ECE 153 FALL QUARTER 2016
ELECTRICAL & COMPUTER ENGINEERING
Course:
ECE 153 Probability and Random Processes for Engineers
URL:
https:/sites.google.com/a/eng.ucsd.edu/ece-153-f2016/
Text:
A. Leon-Garcia, Probability, Statistics and Random Processes for
El
ECE 153 MIDTERM
October 26, 2015
Solution
1. The random variable X has the density
fx(x) =
x - 2 , 1 ~x<oo
cfw_
0,
X 21_
5o Tr.ot-
otherwise.
0~ 't~ l
A new random variable is obtained from X via the transformation
Y~G(X)~ 1-(1/X), I ~X <oo.
I
~1 := 1').
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
is
sh
Th
https:/www.coursehero.com/file/8527032/Solutions-HW2/
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
is
sh
Th
https:/www.coursehero.com/file/8527032/Solutions-HW2/
ar stu
ed d
v