Section 7.1
Conditioning a Random Variable
by an Event
Example 7.1
Let N equal the number of bytes in an email. A conditioning event might
be the event I that the email contains an image. A second kind of conditioning would be the event cfw_N > 100,000, w
Probability and Stochastic Processes
A Friendly Introduction for Electrical and Computer Engineers
Third Edition
INSTRUCTORS SOLUTION MANUAL
Roy D. Yates, David J. Goodman, David Famolari
September 8, 2014
Comments on this Solutions Manual
This solution
Section 3.1
Denitions
Discrete Random Variables
In this chapter and for most of the remainder of this book, we examine probability
models that assign numbers to the outcomes in the sample space.
When we observe one of these numbers, we refer to the obse
Example
/ myfirst.cppdisplays a message
#include <iostream>
/ a
PREPROCESSOR directive
int main()
cfw_
/ function header
/ start of function body
using namespace std;
definitions visible
/ make
cout < Come up and C+ me some time.;
/ insert message into t
Probability and Stochastic Processes
A Friendly Introduction for Electrical and Computer Engineers
SECOND EDITION
Roy D. Yates
David J. Goodman
Definitions, Theorems, Proofs, Examples,
Quizzes, Problems, Solutions
Chapter 2
Probability and Stochastic
Processes
Chapter 1
Extra : r groups of n samples
n indistinguishable samples divided into
r distinguishable groups
r slots
oo oo
oo o o o
oo o
n balls
o oo
ooo o
n + r  1 n + r  1
n = r 1
o
o
r1 bars
CH 9. Memory Models and
Namespaces
1)
2)
youll learn about the following:
Separate compilation of programs
Storage duration, scope, and linkage
3)
Placement new
4)
Namespaces
Separate Compilation
C+, like C, allows and even encourages
you to locate the co
Probability and Stochastic Processes
A Friendly Introduction for Electrical and Computer Engineers
SECOND EDITION
Roy D. Yates
David J. Goodman
Definitions, Theorems, Proofs, Examples,
Quizzes, Problems, Solutions
Chapter 3
Normal Distribution
=
()
= (
CH4. Compound Types
Will learn arrays, strings, getline(), get(),
structures, unions, enumerations, pointers
Dynamic memory with new and delete.
Dynamic arrays, structures
Automatic, static, and dynamic storage
vector and array classes.
Arrays
An array is
CH 1. getting started
C+ joins three separate programming
traditions: the procedural language
tradition, represented by C; the objectoriented language tradition, represented
by the class enhancements C+ adds to
C; and generic programming, supported
by C+
Section 10.1
Sample Mean: Expected Value
and Variance
Denition 10.1 Sample Mean
For iid random variables X1, . . . , Xn with PDF fX(x), the sample mean of
X is the random variable
X + + Xn
.
Mn(X) = 1
n
Sample Mean = Expected Value
The rst thing to notic
Two Types of Statistical
11 Comment: Inference
This chapter contains brief introductions to two categories of statistical inference.
Signicance Testing
Decision Accept or reject the hypothesis that the observations result from a certain
probability model
Section 9.1
Expected Values of Sums
Theorem 9.1
For any set of random variables X1, . . . , Xn, the sum Wn = X1 + + Xn
has expected value
E [Wn] = E [X1] + E [X2] + + E [Xn] .
Proof: Theorem 9.1
We prove this theorem by induction on n. In Theorem 5.11, we
Pairs of Random Variables
In this chapter, we consider experiments that produce a collection of random variables, X1 , X2 , . . . , Xn , where n can be any integer.
For most of this chapter, we study n = 2 random variables: X and Y . A pair of
random va
Estimation
In this chapter we use observations to calculate an approximate value of a sample
value of a random variable that has not been observed.
The random variable of interest may be unavailable because it is impractical to
measure (for example, the
Section 13.1
Denitions and Examples
Denition 13.1 Stochastic Process
A stochastic process X(t) consists of an experiment with a probability
measure P[] dened on a sample space S and a function that assigns
a time function x(t, s) to each outcome s in the
Probability and Stochastic Processes
A Friendly Introduction for Electrical and Computer Engineers
SECOND EDITION
Problem Solutions
July 26, 2004 Draft
Roy D. Yates and David J. Goodman
July 26, 2004
This solution manual remains under construction. The c
Problem Solutions Chapter 2
Problem 2.2.1 Solution
(a) We wish to nd the value of c that makes the PMF sum up to one.
PN (n) =
Therefore,
2
n=0
c(1/2)n n = 0, 1, 2
0
otherwise
(1)
PN (n) = c + c/2 + c/4 = 1, implying c = 4/7.
(b) The probability that N 1
CH10. OBJECTS AND
CLASSES
With a procedural approach, you first
concentrate on the procedures you will
follow and then think about how to
represent the data.
With OOP, you begin by thinking about the
data. Furthermore, you think about the
data not only in
CH 14 Reusing code
Hasa relationships
Classes with member objects
(containment
The valarray template class
Private and protected inheritance
Multiple inheritance
Virtual base classes
Creating class templates
Using class templates
Reuse of code
Public inh
CH 13 inheritance
Inheritance as an isa relationship
How to publicly derive one class from
another
Protected access
Constructor member initializer lists
Upcasting and downcasting
Virtual member functions
Early (static) binding and late (dynamic)
binding
' TWO
 u. «mm». Mm.mu.~mm\..y.~..h~. m.
. mmmmmwmw , . .1
wmv
LESSON
Figure I  The 4001 Quad 2Inpu! NOR Gate
In the previous experiments you built,
using discrete components (transistors,
diodes, resistors), the YES and NOT logic
circuits and t
APPENDIX
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4511 BCD to 7Segment Latch/Decoder/Driver
L_E: mm Enable (Active LOW)
Bl: Banking Inwt (Active LOW)
I3: Lamp Test (Acti
ECE 30200
Fall 2013
Homework #9 Solution
Problem 1. Let random variable Y be an exponential random variable with PDF
y
e , y0
fY (y) =
0,
otherwise
Let the random process X(t) be defined as X(t) = t Y .
1. What is FX(t) (x), the CDF of random process X(t
Midterm Exam 2
Date: Monday, November 11
Time: 3:00PM  4:15PM
Location: In class
Exam Rules
No notes, textbooks, etc.  only paper and
pencils
No calculators
No talking, no passing papers, etc.
Cheating will result in F grade on exam
One script
ECE 30200
Fall 2013
Homework #3
Due: Wednesday, September 25 at the beginning of class
Reading: Yates and Goodman, Chapter 2, Sections 19
Problem 1. Consider the experiment of tossing a fair sixsided die (has 1, 2, 3, 4, 5,
6 dots on each side respectiv
ECE 30200
Fall 2013
Homework #2
Due: Monday, September 16 at the beginning of class
Reading: Chapter 1, Sections 46, 810
Problem 1. Using Axioms of Probability (Axiom 13 as discussed in class) to prove
Theorem 1.7 (d), i.e., if A B, then P (A) P (B).
P
ECE 30200
Fall 2013
Homework #4
Due: Wednesday, October 16 at the beginning of class
Reading: Yates and Goodman, Chapter 3, Sections 18
Problem 1. The cumulative distribution function (CDF) of a continuous random variable Y is given by
y < 2
0,
2
c(y +