Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
EE3025,Spring2013Solutions,HW#5
Instructor:N.Sidiropoulos
Turnpageforsolutions
3.
a)E X
EW
W
EX
EX
Var X
0
EX
EX
EW
E W
EW
W
2 E W W
EW
W
2W W
from the linearity
Bytheway,
EW
1, since E W
0 amd Var W
1
EW
1, since E W
0 amd Var W
1
E W W
0,sinceW and
Statistical Methods in Electrical and Computer Engineering
EE 3025

Fall 2012
EE 3025: Statistical Methods in ECE
Sample Final Exam
Spring 2012
Instructor: Nikos Sidiropoulos
CLOSED BOOK, THREE DOUBLESIDED SHEETS OF PAPER WITH NOTES ALLOWED. CALCULATORS OK. PLEASE BE RIGOROUS AND PRECISE AND SHOW YOUR WORK. THIS
EXAM CONSISTS OF F
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
1
EE 3025, S2013: Homework assignment #2
Assigned: Monday Feb. 4, 2013
Due: Monday Feb. 11, 2013 @ beginning of class
Instructor: N. Sidiropoulos
All problems can be found in pp. 9497, text, but do note below the two extra questions related
to Problems 2
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
2
Problem 1: (35 points) Random variables X and Y have the joint PDF
X
f x ,Y (
)
= cfw_ 2,
0
'Y
X 2: 0, y 2: 0,
other wise
'
(15 points) Find the PDF, mean, and variance of X .
(20 points) Find E [XY] and the correlation coefficient
pectation.
!,xcx) =
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
1
EE 3025, S2013: Homework assignment #3
Assigned: Fri. Feb. 15, 2013
Due: Fri. Feb. 22, 2013 @ beginning of class
Instructor: N. Sidiropoulos
1) Consider again St. Petersburgs paradox we discussed in class: Keep on ipping a coin until it comes
up heads;
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
.
EE 3025: Statistical Methods in ECE
Exam I: Feb. 25, 2013
Instructor: Nikos Sidiropoulos
CLOSED BOOK, ONE DOUBLESIDED SHEET OF PAPER WITH HANDWRITTEN NOTES ALLOWED. CALCULATORS OK. PLEASE BE RIGOROUS AND PRECISE AND SHOW YOUR WORK.
TH IS EXAM CONSISTS
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Homework 7 solution
Exercises: (You must show all of your work for full credit!)
Problem 1:
a) X and Y are not independent. Note:
R 1x
2dy = 2(1 x) 0 x 1
0
fX (x) =
0
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Thursday March 9, 2017
Homework 6 Solutions
Exercises: (You must show all of your work for full credit!)
1) Solutions:
(a) The joint CDF of Y1 , Y2 is
F (y1 , y2 ) = P
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Thursday April 20, 2017
Homework 9 Solutions
Exercises: (You must show all of your work for full credit!)
1) Solutions:
(a) The number of requests in one minute N is a
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Thursday May 4, 2017
Homework 10 Solutions
Exercises: (You must show all of your work for full credit!)
1. Solution:
Given, Yk = q0 + q1 k + q2 k 2 + Zk
Zk is a sequen
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Thursday April 20, 2017
Homework 9 Due Thursday April 27, 2017 at 11:00am
Exercises: (You must show all of your work for full credit!)
1) In any oneminute interval, t
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Thursday April 6, 2017
Homework 7 Due Thursday April 13, 2017 at 11:00am
Exercises: (You must show all of your work for full credit!)
1) Random variables X and Y have
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Homework 8 solution
Exercises: (You must show all of your work for full credit!)
Problem 1:
a) Marginal PDF fY1 ,Y4 (y1 , y4 ) where 0 y1 y4 1 can be calculated as
Z Z
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
EE 3025, Spring 2013 Solutions, HW#4
Instructor: N. Sidiropoulos
Turn page for solutions
1) a)
0
0
e
x 2 y
dxdy = e
2 y
0
dy
0
1
e dx = e 2 y
2
x
0
x 1
1
e
= 1 =
0
2
2
c=2
b)
f x (x ) =
y =0
f x , y ( x, y )dy =
y =0
2e x e 2 y dy = 2e x e 2 y
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
1
EE 3025, S2013: Homework assignment #1
Assigned: Monday Jan. 28, 2013
Due: Monday, Feb. 4, 2013 @ beginning of class
Instructor: N. Sidiropoulos
1)
2)
3)
4)
5)
Problem 1.6.2, text.
Problem 1.6.7, text.
Problem 1.7.5, text.
Problem 1.9.4, text.
a) Prove
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
1
EE 3025, S2013: Homework assignment #9
Assigned: Wed. May 1, 2013
Due: Wed. May 8, 2013 @ beginning of class
Instructor: N. Sidiropoulos
1) Here we revisit the optimal ltering problem (from the viewpoint of minimizing mean squared
error) under the const
Statistical Methods in Electrical and Computer Engineering
EE 3025

Fall 2012
1
EE 3025: Statistical Methods in ECE
Final Exam: Thursday May 10, 2012
1:303:30pm, KH 3210
Instructor: Nikos Sidiropoulos
CLOSED BOOK, THREE DOUBLESIDED SHEETS OF PAPER WITH NOTES ALLOWED. CALCULATORS OK. PLEASE BE RIGOROUS AND PRECISE AND SHOW YOUR W
Statistical Methods in Electrical and Computer Engineering
EE 3025

Fall 2012
.
2
Problem 1: (40 points) According to a recent study, the probability that a randomly drawn person
is preDiabetic is 0.22. The probability that a randomly drawn person has high Cholesterol is 0.15. The
probability that a randomly drawn person is neithe
Statistical Methods in Electrical and Computer Engineering
EE 3025

Fall 2012
1
EE 3025: Statistical Methods in ECE
Final Exam: Thursday May 10, 2012
1:303:30pm, KH 3210
Instructor: Nikos Sidiropoulos
CLOSED BOOK, THREE DOUBLESIDED SHEETS OF PAPER WITH NOTES ALLOWED. CALCULATORS OK. PLEASE BE RIGOROUS AND PRECISE AND SHOW YOUR W
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
.
EE 3025: Statistical Methods in ECE
Final Exam: Fri. May 17,2013, 10:30 AM 12:30 PM
Last name starting from A to L: Go to PHYS 133
Last name starting from M to Z: Go to Vincent Hall, room 16
Duration: 2 hours
Instructor: Nikos Sidiropoulos
CLOSED BOOK,
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
EE3025 Sample Final Exam
Tingting Xu
2013510
Problem 1
Part a) Hint
Y and Z are Gaussian R.V. s with zero mean (WSS)
Bivariate Gaussian PDF (p.191, Def.4.17)
fY ,Z (y, z )
1
2
2 y z 1 y,z
y y
(y y )(z z ) z 2
2
z
(
) 2 y,z
(
)
y
y z
z
exp
2
2(
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
EE 3025: Statistical Methods in ECE
Exam II: Wed. April 3, 2013
10:1011:00am, PHYS 133
Instructor: Nikos Sidiropoulos
CLOSED BOOK, TWO (1 + 1) DOUBLESIDED SHEETS OF PAPER WITH NOTES ALLOWED.
CALCULATORS OK. PLEASE BE RIGOROUS AND PRECISE AND SHOW YOUR W
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
EE 3025: Statistical Methods in ECE
Sample Exam II
Instructor: Nikos Sidiropoulos
CLOSED BOOK, TWO (1 + 1) DOUBLESIDED SHEETS OF PAPER WITH NOTES ALLOWED.
CALCULATORS OK. PLEASE BE RIGOROUS AND PRECISE AND SHOW YOUR WORK. THIS
EXAM CONSISTS OF THREE PROB
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
Syllabus EE 3025: Statistical Methods in Electrical and Computer Engineering
S 2013 / N. Sidiropoulos
Catalog description:
EE 3025  Statistical Methods in Electrical and Computer Engineering (3.0 cr; Prereq[3015, CSE] or
instr approval; fall, spring, su
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
EE 3025, Spring 2013 Solutions, HW#8
Instructor: N. Sidiropoulos
For responses to recitation 12 questions: see commented code in the associated (Rec12) folder in moodle.
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2013
1
EE 3025: Statistical Methods in ECE
Sample Exam I
Instructor: Nikos Sidiropoulos
CLOSED BOOK, ONE DOUBLESIDED SHEET OF PAPER WITH HANDWRITTEN NOTES ALLOWED. CALCULATORS OK. PLEASE BE RIGOROUS AND PRECISE AND SHOW YOUR WORK.
THIS EXAM CONSISTS OF THREE
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Thursday April 27, 2017
Homework 10 Due Thursday May 4, 2017 at 11:00am
Exercises: (You must show all of your work for full credit!)
1) Suppose
Yk = q0 + q1 k + q2 k 2
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Thursday April 13, 2017
Homework 8 Due Thursday April 20, 2017 at 11:00am
Exercises: (You must show all of your work for full credit!)
1) Random variables Y1 , Y2 , Y3
Statistical Methods in Electrical and Computer Engineering
EE 3025

Spring 2014
EE 3025 Statistical Methods in Electrical and Computer Engineering
Spring Semester 2017
Thursday March 9, 2017
Homework 6 Due Thursday March 23, 2017 at 11:00am
Exercises: (You must show all of your work for full credit!)
1) Random variables X1 and X2 are