S2-1
EEL 5544 HW 2 Solutions, Fall 2008
Combinatorics
SS-1.
(a) With order and with repeats, the number of possible combinations (this is a dangerous
word to use here when talking about probabilities)
Homework 2
The following homework set has two types of problems. Those labeled SS are self-study
problems that do not need to be turned in. However, there are problems that I suggest you complete
to e
EEL 5544 Midterm Examination Number 2
November 13, 2008
The time for this test is 2 hours. This is a closed book test, but you are allowed two formula
sheets. The formula sheets cannot contain any exa
Homework 7
SS-1. Let X and Y be independent exponential random variables, with parameters 1 and 2 ,
respectively. Find the density function of Z = |X Y |.
Answer:
fZ (z) =
1 1
(e1 z + e2 z ) u(z)
1 +
EEL 5544 Midterm Examination Number 2
November 12, 2009
The time for this test is 2 hours. This is a closed book test, but you are allowed two formula
sheets. The formula sheets cannot contain any exa
EEL 5544 Midterm Examination Number 1
October 6, 2008
The time for this test is 2 hours. This is a closed book test, but you are allowed one formula
sheet. The formula sheet cannot contain any example
Homework 3
R ANDOM VARIABLES
SS-1. The sample space for a random experiment is shown as the shaded area in the gure below.
All outcomes in S are equally likely. A random variable Y is set equal to the
, ' See Answer key on Iast4 page:
Emiched'Biology - . - ‘ ' ‘ T ' ' " '
Provosthoza '7'.“ a .'
Genetics Problems -
f 1.111 a certain organism, the gene for taII,T, is dominant
genotype and phenotype f
Solutions to Study Problems
EEE 5544 - Noise in Linear Systems
1.
2.
3.
4.
5.
6.
A. Leon-Garcia
INSTRUCTORS SOLUTIONS MANUAL
Probability, Statistics, and Random Processes for Electrical Engineering
10
EEE 5544 Midterm Examination Number 1
October 7, 2015
The time for this test is 2 hours. This is a closed book test, but you are allowed one formula
sheet. The formula sheet cannot contain any example
EEE 5544 Examination Number 3
December 9, 2015
The time for this test is 2 hours. This is a closed book test, but you are allowed three formula
sheets. The formula sheets cannot contain any examples.
S AMPLING WITH REPACEMENT AND WITH ORDERING
Problem: Choose k objects from a set A with
replacement (after each choice, the object is returned
to the set). The ordered series of results is noted.
Resu
EEL 5544 Noise in Linear Systems
Will be renamed to Stochastic Methods in Engineering I
S YLLABUS
1. Catalog Description: (3 credits) Passage of electrical noise and signals through linear
systems. St
L2-1
EEE 5544 Noise in Linear Systems Lecture 2
Motivation
Consider applying the concept of equally-likely outcomes to an innite sample space.
What should the probability of each outcome be?
Suppose
EEE 5544 Noise in Linear Systems
Will be renamed to Stochastic Methods in Engineering I
S YLLABUS
1. Catalog Description: (3 credits) Passage of electrical noise and signals through linear
systems. St
Homework 7
SS-1. X and Y are random variables with joint density function
(
2
2
ce(x +y )/2 , x2 + y2 1
fXY (x, y) =
0,
otherwise,
where c is an appropriately chosen constant.
(a) Find the value of c.
~ v: La 1 k» mm} M (115mg,ny :
4 it» WWW if WM will W UL afx
Em «3 5;; Km mm = {Nam :21 mxfm ,
a.
1L} Z5 W E,me 3x QKQHPQHM
341%: L17 TLL "('wljaww abrw. ./uz, Le-ESgwt
Mk {Li ihi/ 6». 1A A r
Study Problems
1. The continuous-time Gaussian random process X(t) has mean E[X(t)] = X and autocovariance
function
(
cos 4T
, | 2T
CX () =
0,
otherwise.
Let
Y (t) = X(t) + 2X(t T ).
a) Give an expres
EEE 5544/EEL 4516
Lecture Notes
Fall 2016
John M. Shea
August 19, 2016
ii
c John M. Shea, 20002016
Except where noted,
Some images in this work are licensed under various Creative Commons licenses, a
SS-1.
SS-2.
(d)
1.
2. Solution will be posted separately.
SS-3.
(a)
P [|X| < 5, Y > 2, Z 2 2] = P [|X| < 5]P [Y > 2]P [Z 2 2]
= P [5 < X < 5](1 P [Y 2])(1 P [ 2 < Z < 2])
= [FX (5 ) FX (5)][1 FY (2)
Proceedings of the International Symposium On Dynamic Games and Applications,
Wroclaw, Poland, June 2008
Bang-Bang Functions: Universal Approximants
for the Solution of Min-Max Optimal Control
Problem
Noise in Linear Systems
EEL 5544
Fall 2017
Stochastic Methods I
Prof. Sean Meyn
Midterm II
This is a closed-book closed-notes test, with two sheets of notes (double-sided) allowed.
For scratch work y
Proceedings of the IFAC World Congress, Toulouse, France, July 2017
Low Error Operation in Open Loop: Nonlinear
Systems with Time Delay ?
HoLim Choi Jacob Hammer
Department
of Electrical Engineering
Proceedings of the 17th Mediterranean Conference on Control and Automation,
Thessaloniki, Greece, June 24-26, 2009
Control During Feedback Failure: Characteristics of
the Optimal Solution
Debraj Chakr
Stochastic Methods I
Homework 9
Due date: Friday November 17, 11:45 AM
November 12, 2017
Your solutions must be submitted through Canvas as a single PDF document as an attachment in
response to the ho