Soln3-1
SS-1.
Soln3-2
1.
Soln3-3
Soln3-4
Soln3-5
2.
Soln3-6
Soln3-7
SS-2.
Soln3-8
SS-3.
Soln3-9
SS-4.
Soln3-10
SS-5.
(a)
fX (x)dx = 1
Area under triangle of height c and base 2a equals 1
1 (c)(2a) = 1
2
c = 1/a
The
fX (x) =
|ax2| , |x| a
0,
otherwise
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) is 603 = 216, 000.
(b) With order and without repeats,
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 examples. You should write your name on the
formula sheets
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 ensure that you understand all the material in the class
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 examples. You should write your name on the
formula sheet and
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 examples. You should write your name on the
formula sheets
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 y-coordinate of
an outcome s = (x, y).
(a) Find the di
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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 expression for E[X(T )X(2T )] in terms of X and T .
b) Give a
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, as noted. The
license can be viewed at:
CC BY: Creative
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)][1 FZ ( 2 ) + FZ ( 2)]
(b)
P [X > 5, Y < 0, Z = 1] = P
Homework 4
1. A new computerized scan of the liver is used to help identify whether a person has a normal
liver (N), benign tumors (B), or liver cancer (C). The computer will automatically classify
the output to indicate tumors (T ) or no tumors (T ).
For
Homework 3
This homework assignment will count double (20 points versus the standard 10 points).
In this assignment, you will use Monte Carlo simulation to estimate probabilities. Here,
Monte Carlo refers to the location of a famous casino in Europe. In M
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 ensure that you understand all the material in the class
Homework 6
Use Monte Carlo simulation (using Python 3) or analysis to solve the following problem. At
least 3 digits of accuracy are required in your answer. Submit a Jupyter Notebook and/or a PDF
containing your work.
A casino hosts the following variati
Homework 9
SS-1. Show that for optimal linear prediction of X given Y, the mean-square error is X2 (1 2 ).
1. Let X and Y be random variables with joint density
(
15x2 y, 0 x y 1
fXY (x, y) =
0,
otherwise
(a) Find the best MMSE estimator for X given Y .
(
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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. Statistical representation of random signals, electrical