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, EE494/EE501, Fall 2014
g
Due in class on Wed, Dec 3rd 2014
Homework 71
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation. S
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Nov 26th 2014
Homework 61
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Nov 12th 2014
Homework 51
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Nov 6th 2014
Homework 41
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation. S
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Oct 22nd 2014
Homework 31
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Oct 8th 2014
Homework 21
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation. S
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Oct 1st 2014
Homework 11
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation. S
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Dec 31st 2014
Homework 91
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
(/9 u(t) = m(t)c(t) =A(SinC(t)+SiI1C2(t))COS(27cht)
Taking the Fourier transform of both sides, we obtain
Um = §[n<f>+A<f)1*<a<f -fc) + 6(f +fc))
= gumfa)+A<f~fc>+n<f+fa+A<f+fc>1
H(ffc) at 0 for lffcl < whereas A(ffc) i Ofor [ffcl < 1. Hence, the band
236 Probability and Random Processes Chapter 5
excited by a stationary random process, the system output is also stationary. In such a case,
we related the aurocorrelation and power spectral density of the LTI system output to the
autocorrelation and pow
1
Bilkent University
EEE-431 Telecommunications I
Fall 2013 - Homework 2
Due: October 8, 2013 (9:30 for Section I, 10:30 for Section II)
1) Please solve 5.22
2) Please solve 5.29
3) Consider the entropy of a discrete memoryless source (DMS) with N possibl
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 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. 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 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 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 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, EE494/EE501, Fall 2014
g
Due in class on Wed, Dec 31st 2014
Homework 91
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Dec 10th 2014
Homework 81
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Dec 3rd 2014
Homework 71
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation. S
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Nov 26th 2014
Homework 61
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Nov 12th 2014
Homework 51
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Nov 6th 2014
Homework 41
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation. S
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Oct 22nd 2014
Homework 31
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation.
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Oct 8th 2014
Homework 21
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation. S
Ozyein University, EE494/EE501, Fall 2014
g
Due in class on Wed, Oct 1st 2014
Homework 11
Please observe academic honesty in preparing your homework. You can ask each other for help when
you need it, but the nal solution should be your own preparation. S