zyein University
Department of Electrical and Electronics
Engineering
EE 450/550 WIRELESS NETWORKS
HOMEWORK #2 (due 20 April 2015)
1. Summarise the main features of 3rd generation mobile phone systems. How do they
achieve higher capacities and higher data

Ozyegin Univ. EE503 Spring 2015
Due 5pm, May 20, 2015
Please scan and send your homework to my e-mail: ali.ercan@ozyegin.edu.tr
Homework 9
1. Consider the following discrete time random process:
X0 N (0, a)
Xn = 1 Xn1 + Zn ,
2
n 1,
where Z1 , Z2 , Z3 , .

Ozyein University
g
EE503 - Stochastic Processes - Spring15
Midterm 3 Solutions
Question 1 - Wiener Process (25 Points)
Suppose X(t) is a Weiner Process (Brownian Motion) with zero mean and autocovariance
function CX (t1 , t2 ) = min(t1 , t2 ). Assume t0

Ozyegin Univ. EE503 Spring 2015
Due 5pm Apr. 25, 2015
Homework 7
Please scan and send your homework to my e-mail: ali.ercan@ozyegin.edu.tr
1. In the lecture it was stated that conditionals of a Gaussian random vector are Gaussian. In this
problem you will

Ozyegin Univ. EE503 Spring 2015
Due 5pm, May 20, 2015
Please scan and send your homework to my e-mail: ali.ercan@ozyegin.edu.tr
Homework 9
1. Consider the following discrete time random process:
X0 N (0, a)
Xn = 1 Xn1 + Zn ,
2
n 1,
where Z1 , Z2 , Z3 , .

Ozyegin Univ. EE503 Spring 2015
Due 5pm Apr. 15, 2015
Homework 6
Please scan and send your homework to my e-mail: ali.ercan@ozyegin.edu.tr
1. Radar signal detection. The received signal S for a radar channel is 0 if there is no target and a random
variabl

Ozyegin Univ. EE503 Spring 2015
Due in class of Mar. 5, 2015
Homework 2
1. Let X be a random variable with the cdf shown below.
F (x)
1
2/3
1/3
1 2
x
3
x
1
2
3
4
Find the probabilities of the following events.
(a) cfw_X = 2.
(b) cfw_X < 2.
(c) cfw_X = 2 c

Ozyegin Univ. EE503 Spring 2015
Due 5pm Apr. 25, 2015
Homework 7
Please scan and send your homework to my e-mail: ali.ercan@ozyegin.edu.tr
1. In the lecture it was stated that conditionals of a Gaussian random vector are Gaussian. In this
problem you will

Ozyegin Univ. EE503 Spring 2015
Due in class Apr. 9, 2015
Homework 5
1. Let X U[0, 1] and Y N (0, X 2 ). Find E XY 2 .
Solution:
1
E XY 2 = E E XY 2 |X
= E X E Y 2 |X
x3 dx =
= E XX 2 = E X 3 =
0
1
.
4
2. Let and X be random variables with
f () =
2
5 3
3

Ozyegin Univ. EE503 Spring 2015
Due in class Apr. 2, 2015
Homework 4
1. Function of uniform random variables.
Let X and Y be two independent U[0, 1] random variables. Find the probability density function (pdf)
of Z = [(X + Y ) mod 1] (i.e., Z = X + Y if

Ozyegin Univ. EE503 Spring 2015
Due 5pm Apr. 15, 2015
Homework 6
Please scan and send your homework to my e-mail: ali.ercan@ozyegin.edu.tr
1. Radar signal detection. The received signal S for a radar channel is 0 if there is no target and a random
variabl

Ozyegin Univ. EE503 Spring 2015
Due in class of Feb. 26, 2015
Homework 1
1. Monty Hall. Gold is placed behind one of three curtains. A contestant chooses one of the curtains.
Monty Hall, the game host, opens an unselected empty curtain. The contestant can

Ozyegin Univ. EE503 Spring 2015
Due in class Mar. 12, 2015
Homework 3
1. Consider the Laplacian random variable X with pdf f (x) = 1 e|x| .
2
(a) Sketch the cdf of X.
(b) Find Pcfw_|X| 2 or X 0 .
(c) Find Pcfw_|X| + |X 3| 3 .
Solution:
(a) We consider two

Ozyegin Univ. EE503 Spring 2015
Due in class, May 14, 2015
Homework 8
1. Digital modulation using PSK: The data to be modulated, cfw_Xn : n 0 , is modeled by a Bernoulli
process with p = 1/2. Dene the discrete-time phase process cfw_n : n 0 by
n =
+
2
if

Ozyegin Univ. EE503 Spring 2015
Due in class Apr. 9, 2015
Homework 5
1. Let X U[0, 1] and Y N (0, X 2 ). Find E XY 2 .
2. Let and X be random variables with
f () =
2
5 3
3
01
0
otherwise
and X|cfw_ = Exp(). Find E(X).
3. Which of the following matrices

Ozyegin Univ. EE503 Spring 2015
Due in class Mar. 12, 2015
Homework 3
1. Consider the Laplacian random variable X with pdf f (x) = 1 e|x| .
2
(a) Sketch the cdf of X.
(b) Find Pcfw_|X| 2 or X 0 .
(c) Find Pcfw_|X| + |X 3| 3 .
1
2. Let X be a r.v. with Lap

Ozyegin Univ. EE503 Spring 2015
Due in class of Feb. 26, 2015
Homework 1
1. Monty Hall. Gold is placed behind one of three curtains. A contestant chooses one of the curtains.
Monty Hall, the game host, opens an unselected empty curtain. The contestant can

Ozyein University
g
EE503 - Stochastic Processes - Spring15
Midterm 2 Solutions
Question 1 - Estimation (40 Points)
y
2
Consider the joint pdf of the random variables X and Y
given on the right. That is,
fX,Y (x, y) =
2
3,
0,
0 x 2 y, 0 y 1,
otherwise.
1

Ozyegin Univ. EE503 Spring 2015
Due in class, May 14, 2015
Homework 8
1. Digital modulation using PSK: The data to be modulated, cfw_Xn : n 0 , is modeled by a Bernoulli
process with p = 1/2. Dene the discrete-time phase process cfw_n : n 0 by
n =
+
2
if

Ozyein University
g
EE503 - Stochastic Processes - Spring15
Midterm 1 Solutions
Question 1 - Two Random Variables (50 Points)
y
2
Consider the joint pdf of the random variables X and Y
given on the right. That is,
fX,Y (x, y) =
0 x 2 y, 0 y 1,
otherwise.