American College of Computer & Information Sciences
ECON 202

Fall 2012
A Fuzzy Comprehensive Evaluation Model for
Harms of Computer Virus
Cong Zheng Lansheng Han* Jihang Ye Qiwen Liu Mengsong Zou
Laboratory for Information Security, School of Computer Science and Technology
Huazhong University of Science and Technology, Wuha
American College of Computer & Information Sciences
fin
ECON 123

Spring 2013
Chapter 13Responsibility Accounting, Support Department Allocations, and Transfer
Pricing
MULTIPLE CHOICE
1. Which of the following is more characteristic of a decentralized than a centralized business structure?
a. The firm's environment is stable.
b. Th
American College of Computer & Information Sciences
Palaka
ECON 297

Spring 2013
Chapter 13Responsibility Accounting, Support Department Allocations, and Transfer
Pricing
MULTIPLE CHOICE
1. Which of the following is more characteristic of a decentralized than a centralized business structure?
a. The firm's environment is stable.
b. Th
American College of Computer & Information Sciences
Queueing
ECON 110

Spring 2012
LIMIT THEOREMS 1. Markovs inequality: far above its mean. A nonnegative random variable is unlikely to be
For any nonnegative random variable X, for a > 0. P (X a) a Note that we do not need to know , and we do not need to know how X is distributed. It
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
ErlangB
Just enter the Arrival and Service Rates.
ErlangB shows the probability of an event being lost.
Arrival Rate () =
Service Rate () =
50 msgs/sec
20 msgs/sec
Copyright 20002001, Pentagon Computer Consultants Ltd.
Traffic Intensity (A) =
Servers N
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
Associated Topics  Dr. Math Home  Search Dr. Math
MeanVariance Ratio of the Poisson Distribution
Date: 03/27/2001 at 19:08:10
From: Jocelyn
Subject: Proof of mean/variance = 1 for Poisson
I would like to show that V(X)/E(X) = 1 for the Poisson distribu
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
J EWISHMATHEMATICIANS
J INFO.ORG
SHORT LIST
Abram Besicovitch
Salomon Bochner
Georg Cantor 6
Paul Cohen
Richard Courant
Joseph Doob
Samuel Eilenberg
Gotthold Eisenstein
Paul Erds
Izrail Gelfand
Alexander Grothendieck 11
Jacques Hadamard
Felix Hausdorff
Er
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
Math 461
Introduction to Probability
A.J. Hildebrand
Variance, covariance, correlation, momentgenerating functions
[In the Ross text, this is covered in Sections 7.4 and 7.7. See also the Chapter Summary on pp. 405407.] Variance: Definition: Var(X) = E(X
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
A Measure Theory Tutorial (Measure Theory for Dummies)
Maya R. Gupta
[email protected]
Dept of EE, University of Washington
Seattle WA, 981952500
UWEE Technical Report
Number UWEETR20060008
May 2006
Department of Electrical Engineering
Univer
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
Transpose
Transpose adaptive routing algorithm for regular mesh
Abstract
In this report, I propose three new adaptive routing algorithms. I named them, Xfirst, Yfirst, and transpose adaptive routing algorithms. Xfirst increases congestion in Xdirection
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
The Normal Distribution on the TI83
The TI83 can perform several statistical functions. Press the [2nd] and [VARS] keys to get to the DISTR menu, here are several of the statistical functions of the calculator.
1. The first choice, normalpdf gives youre
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
ST202 PDTI
Series
Useful Series and Expansions
1. Taylor series: for a function f with continuous derivatives, j th derivative denoted f (j ) ;
f (x) = f (a) + f (a)(x a) +
1
1
f (a)(x a)2 + . . . + f (j ) (a)(x a)j + . . .
2!
j!
2. MacLaurin Series: Tayl
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
SETIT 2005
3rd International Conference: Sciences of Electronic,
Technologies of Information and Telecommunications
March 2731, 2005 TUNISIA
Congestion Level Prediction of SelfSimilar Traffic
Based On Wavelet Transform
Abbasi.Z 1*,Noroozi.F 2* and Shari
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
1
Contract no: BAP098MRG15Med
Probability Theory
J.M. Steele
Wharton
Probability theory is that part of mathematics that aims to provide insight into phenomena that depend on chance or on uncertainty. The most prevalent use of the
theory comes through
American College of Computer & Information Sciences
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ECON cse110

Spring 2012
2. The Poisson Process
A counting process cfw_N (t), t 0 is a Poisson
process with rate if . . .
Denition 1.
(i) N (0) = 0,
(ii) N (t) has independent increments,
(iii) N (t) N (s) Poisson (t s) for s < t.
This can be shown to be equivalent to
Denition 2.
American College of Computer & Information Sciences
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ECON cse110

Spring 2012
Counting Processes
Renewal Processes/Counting Processes/Poisson Processes
N(t)
'
: family of random variables
: number of arrivals in interval
.
with probability 1
: family of nonnegative integer
Counting Process
valued random variables (one for each
) w
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
C
H
12
A
P
T
E
R
Overview of
Linear Regression
P
art II contains the statistical theory of the OLS estimation. This theory rests on three
basic assumptions about the sampling distribution from which one observes the data in the
LHS variable y and the RHS
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
ST2238 Introductory Biostatistics
Probability distribution function for the standard Normal distribution
These give the cumulative probability F that X is less than x, where X is a normally distributed variate with
mean 0 and standard deviation 1.
x
0.00
American College of Computer & Information Sciences
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ECON cse110

Spring 2012
Virtual Laboratories > 4. Special Distributions > 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5
2. The Normal Distribution
The normal distribution holds an honored role in probability and statistics, mostly because of the central limit theorem,
one of the fun
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
Statistics, Probability and Decision Making: The Normal Distribution
Name _ Period _
Date _
The Normal Distribution
Read the following about the importance of the normal distribution. (Modified
from Wikipedia: http:/en.wikipedia.org/wiki/Normal_distributi
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
Nonnegative Integer Valued Random Variables
H. Krieger, Mathematics 156, Harvey Mudd College
Fall, 2008
Let N be a random variable with values from the set cfw_+, 0, 1, 2, . . .. Then
N is referred to as a nonnegative integer valued random variable. Let
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
Lecture 25: Moment Generating Functions
1.) Denition and Properties
Earlier, we dened the probability generating function of a nonnegative integervalued random
variable X to be the function
X (s) = E sX
Pcfw_X = nsn .
=
n=0
In this section, we will intr
American College of Computer & Information Sciences
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ECON cse110

Spring 2012
Lecture 6.5
In this lecture Poisson processes are derived from rst principles and the notion of Markov chains
is extended to include continuous time Markov chains. This is necessary for our original aim of
modelling the M/M/1 queue with Markov chains (rem
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
INTEGRATION BY PARTS
Integration by parts is a technique used to solve integrals that fit the form:
u dv
This method is to be used when normal integration and substitution do not work.
The integrand must contain two separate functions. For example,
x(co
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
From Ronald Meester, A natural introduction to Probability theory, page 110.
Denition A function g is said to be regular if there exist numbers <
a1 < a0 < a1 < with ai and ai when i , so that g is
continuous and monotone on each interval (ai , ai+1 ).
Th
American College of Computer & Information Sciences
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ECON cse110

Spring 2012
Julio L. Peixoto  September 1999
INDEPENDENCE AND UNCORRELATION
(Some random comments motivated by class discussion.)
Statistical Independence
1. Random variables y1 , y 2 , , y n are said to be (statistically) independent if knowledge
about one or sever
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
Network Modeling and Simulation: Homework 4
Due in class by: Sat, April 24, 2010
Solve problems 4.9, 4.11, 4.16, 4.21, 4.23, 4.24, 4.25, 4.29, 6.10, 6.14, 6.26, 7.12, 8.1, 8.8, and
8.11 in the Averill book.
1
American College of Computer & Information Sciences
Queueing
ECON cse110

Spring 2012
Network Modeling and Simulation: Homework 3
Due in class by: Sat, April 10, 2010
Solve problems 4.1, 4.2, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.15, 4.17, 4.18, and 4.19 in the Schwartz
book.
1