PROBABILITY AND STOCHASTIC PROCESSES
A FRIENDLY INTRODUCTION FOR ELECTRICAL AND COMPUTER ENGINEERS
Third Edition
Chapter 3 Viewgraphs
Roy D. Yates & David J. Goodman
Yates & Goodman 3e
62
Discrete Random Variables
In this chapter and for most of the rema
Yates & Goodman 3e
Theorem 2.2
The number of kpermutations of n distinguishable objects is
(n)k = n(n
1)(n
2) (n
k + 1) =
n!
(n
k)!
.
41
Yates & Goodman 3e
42
Theorem 2.3
The number of ways to choose k objects out of n distinguishable objects
is
n
k
=
(
Yates & Goodman 3e
Section 3.5
Averages and Expected Value
80
Yates & Goodman 3e
80
Example 3.23 Problem
For one quiz, 10 students have the following grades (on a scale of 0 to
10):
X
,
Xn
X2
9, 5, 10, 8, 4, 7, 5, 5, 8, 7

.
(1)

57
Find the mean, the m
Formula Sheet Probability and Random Processes
Continuous Sample Space:
The Cumulative Distribution Function (CDF):
F X ( x )=P [ X x ]
(Less Than Or Equal To!)
For any random variable X,
F X ( )=0, F X ( )=1, P[ x 1< X < x 2=F X ( x 2 )F X ( x 1 ) ]
Prob
Yates & Goodman 3e
11
Denition 1.4 Axioms of Probability
A probability measure P[] is a function that maps events in the sample
space to real numbers such that
Axiom 1 For any event A, P[A]
0.
Axiom 2 P[S] = 1.
Axiom 3 For any countable collection A1, A2,
Yates & Goodman 3e
Section 2.1
Tree Diagrams
35
Yates & Goodman 3e
Problem 2.1.5
57
Suppose that for the general population, 1 in 5000 people carries the human immunodeciency virus (HIV). A test for the presence of HIV yields
either a positive (+) or nega
Yates & Goodman 3e
20
Theorem 1.8
For a partition B = cfw_B1, B2, . . . and any event A in the sample space, let
Ci = A \ Bi. For i 6= j, the events Ci and Cj are mutually exclusive and
A = C1 [ C2 [ .
Yates & Goodman 3e
Theorem 1.9
For any event A, and p
PROBABILITY AND STOCHASTIC PROCESSES
A FRIENDLY INTRODUCTION FOR ELECTRICAL AND COMPUTER ENGINEERS
Third Edition
Chapter 7 Viewgraphs
Roy D. Yates & David J. Goodman
Yates & Goodman 3e
Section 7.1
Conditioning a Random Variable
by an Event
242
Yates & Goo
PROBABILITY AND STOCHASTIC PROCESSES
A FRIENDLY INTRODUCTION FOR ELECTRICAL AND COMPUTER ENGINEERS
Third Edition
Chapter 3 Viewgraphs
Roy D. Yates & David J. Goodman
Yates & Goodman 3e
62
Discrete Random Variables
In this chapter and for most of the rema
Yates & Goodman 3e
66
Probability Mass Function
Denition 3.3 (PMF)
The probability mass function (PMF) of the discrete random variable X
is
PX (x) = P [X = x]
Yates & Goodman 3e
68
Families of Random Variables
In practical applications, certain families
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