1
NAME
ISyE 6739 Test 1a Solutions Summer 2012
This test is 100 minutes long. You are allowed one cheat sheet.
1. What do you call a nite sample space in which all of the outcomes are equally
likely?
Solution: simple.
2. TRUE or FALSE? A B = A B.
Solut
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IE 535 Summer 2014
Homework #2 Due Tuesday, July 29
(Do as many of the following problems as you feel comfortable with.)
1. Use the basic Monte Carlo technique from class to integrate
1
I =
exp(x2 ) dx.
0
(a) Use n = 100 Unif(0,1) random variates to pro
1
ISyE 6739 Test 2 Solutions Summer 2012
This test is 100 minutes long. You are allowed two cheat sheets. Only write nal answers!
All parts of all questions are 3 points each.
1. A box contains 2 red, 3 black, and 5 blue sox. Suppose 6 sox are selected on
SIMAN Run Controller.
80.230204 Minutes>
ARENA Simulation Results
A - License: STUDENT
Summary for Replication 1 of 10
Project: Call Center Run execution date : 7/22/2014
Analyst: Ernistine Model revision date: 7/22/2014
Replication ended at time : 80.
1
NAME
ISyE 6644 Test #3 Solutions
Spring 2004 (revised 12/7/13)
Open book, open notes. You have 60 minutes.
1. (30 points) Consider the continuous Pareto distribution, whose p.d.f. is given by
f (x) = a x(+1) ,
where x a 0 and > 0. (The constant a is kn
1
NAME
IE 535 Summer 2014 Test #1 Solutions
This test is 90 minutes and is open book, open notes.
1. If X Pois(3), nd E[3X 2 2].
Solution: 3E[X 2 ] 2 = 3 Var(X) + (E[X])2 2 = 38.
1
2. Suppose X has p.d.f. f (x) = 3x2 , 0 < x < 1. Find E[ X 2 ].
1
Solutio
Generating Uniform Random Numbers
Christos Alexopoulos and Dave Goldsman
Georgia Institute of Technology, Atlanta, GA, USA
October 21, 2013
1 / 43
Outline
1
Introduction
2
Some Generators We Wont Use
3
Linear Congruential Generators
4
Tausworthe Generator
Selecting the Best System
Dave Goldsman
School of ISyE
Georgia Institute of Technology
Atlanta, GA, USA
[email protected]
December 6, 2013
1 / 67
Outline
1 Introduction
2 Find the Normal Distribution with the Largest Mean
Motivation
Single-Stage Procedure
T
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NAME
ISyE 6644 Test 2 Additional Practice Fall 2013
This test is open notes, open books. You have 90 minutes. Good Luck!
1. (3 pts each) Short-answer questions on less-recent topics Just write your answer.
(a) If X and Y have joint p.d.f. f (x, y) = cx
1 NAME
ISyE 6644 - Test #2
Spring 2007
This is an optional take-home test. Questions 135 are short answer questions (just write your answer) and are worth 2 points each. Questions 3640 are "regular" questions, each worth 6 points. Try not to spend more t
1 NAME
ISyE 6644 - Fall 2008 - Test #2 Solutions
This test is open book, open notes. You have 85 minutes. Do not show any work other than your answers on this sheet. Good luck! Put your answers here. (1) (4) (7) (10) (13) (16) (19) (22) (25) (28) (31) (2
1 NAME
ISyE 6644 Test 2 Solutions Summer 2007
This test is open notes, open books. Good Luck! 1. (75 points) Short-answer questions on random number and variate generation. Suppose that U and U1 , U2 , . . . are i.i.d. U (0, 1). (a) If we use the generat
1
NAME
IE 535 Test 2 Summer 2014
This is a take-home test, but please dont spend more than a few hours on it. Note that
all work must be your own, so do not discuss the test with anyone else. If you have
any questions, just email or Skype me. Circle all
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NAME
ISyE 6739 Test 3 Solutions Summer 2012
This test is 100 minutes long. You are allowed three cheat sheets plus distribution tables.
1. A die is thrown 7 times. Find P(3 comes up at least once).
Solution: 1 P(no 6s appear) = 1 (5/6)7 = 0.721.
2. A d
1 NAME
ISyE 6644 - Summer 2007 - Test #1 Solutions
This test is open book, open notes. You have 85 minutes. Good luck! Put your answers here. 1. (a) (d) (g) (j) (m) (p) (s) (v) (y) 2. (a) (d) (b) (e) (c) (b) (e) (h) (k) (n) (q) (t) (w) (c) (f) (i) (l) (o
1
NAME
ISyE 6644 Spring 2012 Test #1 Solutions
This test is open book, open notes. Just show your answers. Good luck!
1. Suppose X has p.d.f. f (x) = 2x, 0 < x < 1. Find E[3X 2].
Solution: E[X ] =
1
0
x 2x dx = 2/3. Thus, E[3X 2] = 4.
2
1
2. Suppose X ha
1
NAME
ISyE 6644 Summer 2009 Test #1 Solutions
This test is open book, open notes. You have 90 minutes. Good luck!
1. Short-answer probability questions.
(a) Suppose X has p.d.f. f (x) = 3x2 , 0 < x < 1. Find E[3X + 2].
Solution: E[X ] =
1
0
x3x2 dx = 3/
1
NAME
ISyE 6644 Test #3 Solutions
Spring 2007
Open book, open notes. You have two hours. Good luck!
Short answer questions Just write your answer.
1. Consider the pseudo-random number generator Xi = (3Xi1 + Xi2 + 2)mod(5)
with seeds X0 = 0 and X1 = 1. F
Modeling Basic Operations and Inputs
Chapter 4
Last revision June 7, 2003
Simulation with Arena, 3rd ed.
Chapter 4 Modeling Basic Operations and Inputs
Slide 1 of 66
What Well Do .
Model 4-1: Electronic assembly/test system
Modeling approaches New Arena
Introduction to Arena
Dave Goldsman
Georgia Tech
Atlanta, GA, USA
[email protected]
www.isye.gatech.edu/~sman
(thanks to Seong-Hee Kim and Barry Nelson)
5/21/2010
DG,SHK,BLN
1
Overview
We now move to the design and
analysis of dynamic systems that evolve
th
Simulation Input Modeling:
Specifying Distributions &
Model Parameters
Christos Alexopoulos
David Goldsman
School of Industrial & Systems Engineering
Georgia Tech
2 July 2012
1
Overview
p
p
p
Deterministic vs. random inputs
Data collection
Distribution fi
1
NAME
ISyE 6644 Spring 2012 Test #2 Solutions
1. Short-answer Arena questions.
(a) TRUE or FALSE? In Arena, it is possible to schedule 10 customers to show
up at the same time.
Solution: TRUE.
2
(b) Which Arena template contains a SEIZE block (i.e., not
1
IE 535 Summer 2014
Homework #1 Due Tuesday, July 8
Do as many of the following problems as you feel comfortable with. The idea is just
to give you an overview of some of the probability machinery that youll encounter later
on in the class. If you have a
1
IE 535 Summer 2014
Homework #1 Solutions
Do as many of the following problems as you feel comfortable with. The idea is just
to give you an overview of some of the probability machinery that youll encounter later
on in the class. If you have any trouble
1. Probability Basics
Dave Goldsman
Georgia Institute of Technology, Atlanta, GA, USA
5/12/14
Goldsman
5/12/14
1 / 98
Outline
1
Intro / Examples
2
Set Theory
3
Experiments
4
Probability
5
Finite Sample Spaces
6
Counting Techniques
7
Counting Applications
Probability and Statistics Review
Dave Goldsman
Georgia Institute of Technology, Atlanta, GA, USA
1/12/14
1 / 58
Outline
1
Preliminaries
2
Simulating Random Variables
3
Great Expectations
4
Functions of a Random Variable
5
Jointly Distributed Random Varia
1 NAME
ISyE 6644 - Fall 2007 - Test #1 Solutions
(Revised 10/16/07) This test is open book, open notes. You have 85 minutes. Good luck! Put your answers here. 1. (a) (d) (g) (j) (m) (p) (s) (v) (y) 2. (a) 3. (a) (d) (b) (e) (h) (k) (n) (q) (t) (w) (z) (b
1
NAME
ISyE 6644 Fall 2008 Test #1 Solutions
(Revised 5/27/09)
This test is open book, open notes. You have 85 minutes. Good luck!
Put your answers here.
1. (a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
(t)
(u)
(v)
(w)
(x)
2