1
ISyE 6644 Spring 2012
Homework #5 Solutions
1. Do some of the following random number generation problems from Law, pp. 419
421: #7.1, 7.2(a), 7.3(d), 7.11, 7.12, 7.13.
Problem 7.1: If Xi+1 = (5Xi + 3)mod(16) nd X500 .
Solution: X0 = 7. Then X1 = 38 mod
1
ISyE 6644 Spring 2012
Homework #6 Solutions
1. Suppose the c.d.f. of X is F (x) = x4 /16, 0 x 2. Develop a generator for X .
Demonstrate with U = 0.54.
Solution: Set F (X ) = U U (0, 1). Then U = X 4 /16, and so X = 2U 1/4 . 2
For U = 0.54, we get X = 1
1
ISyE 6644 Fall 2015
Homework #3 Due Tuesday 9/22/15
In what follows, well work with a couple of the Arena models we introduced during lecture.
The models referenced below are from my webpage,
www.isye.gatech.edu/sman/courses/6644/.
1. Arena Baby Model 3
1
ISyE 6644 Spring 2012
Homework #2 Solutions
1. Suppose that X is a discrete random variable having probability function
Pr(X = k ) = ck 2 for k = 1, 2, 3. Find c, Pr(X 2), E[X ], and Var(X ).
Solution. Since
1=
3
Pr(X = k ) =
3
ck 2 = 14c,
k=1
k=1
2
2
2
ISyE 6414: Regression Analysis
HW#3 (due in class on Friday, June 07, 2013)
There are 3 questions, and please look at both sides. Total points = 20 + 30 + 30 = 80 pts.
(It is OK to use R or other statistical softwares for this homework.)
1. Employee Salar
1
ISyE 6644 Simulation Spring 2010
Professor: Dave Goldsman; Oce: Groseclose 433; Phone: 404-894-2365; email:
[email protected]; website: www.isye.gatech.edu/sman/courses/6644.
Class Times and Location: This is a Distance Learning course.
Oce Hours: Wheneve
Calculus, Probability, and Statistics Primers
Dave Goldsman
Georgia Institute of Technology, Atlanta, GA, USA
8/28/16
1 / 92
Outline
1 Calculus Primer
2 Probability Primer
Basics
Simulating Random Variables
Great Expectations
Functions of a Random Variabl
Generating Uniform Random Numbers
Christos Alexopoulos and Dave Goldsman
Georgia Institute of Technology, Atlanta, GA, USA
10/13/16
1 / 41
Outline
1
Introduction
2
Some Lousy Generators We Wont Use
3
Linear Congruential Generators
4
Tausworthe Generator
5
1
ISyE 6644 A,Q Simulation Fall 2016
(revised 9/8/16)
Class Times and Place: T 3:05P4:25P, Weber SST III Room 1.
Instructor: Dave Goldsman; Groseclose 433; email [email protected]; website
www.isye.gatech.edu/sman; phone 404-894-2365 (office), 404-822-8949
Hand and Spreadsheet Simulations
Christos Alexopoulos and Dave Goldsman
Georgia Institute of Technology, Atlanta, GA, USA
9/8/16
1 / 34
Outline
1
Stepping Through a Differential Equation
2
Monte Carlo Integration
3
Making Some
4
Single-Server Queue
5
(s,
1
NAME
ISyE 6644 Test 3 Solutions Fall 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). If I ask you to name a rand
1
NAME
ISyE 6644 Test 3 Solutions Spring 2012
(revised 12/7/13)
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 (
1
NAME
ISyE 6644 Fall 2013 Test #3 Solutions
This test 2 hours. You are allowed three cheat sheets. Every question is 2.5 points. Only
turn in this answer page. Only turn in succinct answers. Good luck!
1. If X and Y have joint p.d.f. f (x, y) = c(1 x)y,
1
NAME
ISyE 6644 Test 3 Solutions Fall 2008
(revised 12/5/13)
This test is open notes, open books. You have 90 minutes. Good Luck!
1. (3 pts each) Short-answer questions on various topics.
(a) If X and Y have joint p.d.f. f (x, y) = cxy 2 , 0 x 1, 0 y 1,
1
ISyE 6644 Spring 2012 Projects from A to Z
Due by the end of Finals Week
The following is a list of suggested projects for ISyE 6644. Pick one project that you nd
interesting. The projects are all intended to be a little open-ended, but do not pick a
pr
General Simulation Principles
Christos Alexopoulos and Dave Goldsman
Georgia Institute of Technology, Atlanta, GA, USA
9/13/16
1 / 22
Outline
1
Steps in a Simulation Study
2
Some Definitions
3
Time-Advance Mechanisms
4
Two Modeling Approaches
5
Simulation
1
ISyE 6644 Fall 2016
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 troubl
1
ISyE 6644 Fall 2016
Homework #2 Solutions
1. Consider the dierential equation f 0 (x) = (x + 1)f (x) with f (0) = 1. Solve this
approximately via Eulers method using increment h = 0.01 for x 2 [0, 0.20].
Solution. You can actually get the true answer us
1
ISyE 6644 Fall 2016
Homework #4 Solutions
1. Do some of the following random number generation problems from Law, pp. 419
421: #7.1, 7.2(a), 7.3(d), 7.11, 7.12, 7.13.
Problem 7.1: If Xi = (5Xi1 + 3)mod(16) find X500 .
Solution: X0 = 7. Then X1 = 38 mod(
1
ISyE 6644 Fall 2016
Homework #6 Due Tues., Nov. 3
1. Generate and plot 10000 bivariate normal random variates (X, Y ), where both X
and Y are standard normal but such that the correlation between X and Y is 0.9.
2. Lets look at a first-order autoregress
1
ISyE 6644 Fall 2016
Homework #2 Solutions
1. Consider the differential equation f 0 (x) = (x + 1)f (x) with f (0) = 1. Solve this
approximately via Eulers method using increment h = 0.01 for x [0, 0.20].
Solution. You can actually get the true answer us
Kedia, Devesh GTID # 902913327
Problem 6
a)
H0: The number of injuries per month follows a Poisson distribution
H1: The number of injuries per month does not follow a Poisson distribution
mjfj
Arrivals
Frequency
0
1
2
3
4
5
6
7 or more
Total
35
40
13
6
4
Total average number out: 784
Parts
Total average cycle time
Part 1
114.75
Part 2
142.04
Part 3
114.67
Part 4
93.479
Minimum value
39.942
61.344
32.8516
29.3531
Maximum Value
297.4
314.16
292.83
268.22
A Whirlwind Tour of Computer
Simulation
Dave Goldsman
Georgia Tech
Atlanta, GA, USA
[email protected]
www.isye.gatech.edu/~sman
5/31/16
1
Outline
1.
2.
3.
4.
5.
6.
Intro to Simulation
Some Easy Examples
Generating Randomness
Analyzing Randomness
Some Bigger
1
ISyE 6644 Fall 2016
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 troubl
1
ISyE 6644 Fall 2016
Homework #5 Solutions
1. Suppose the c.d.f. of X is F (x) = x3 /8, 0 x 2. Develop a generator for X.
Demonstrate with U = 0.54.
Solution: Set F (X) = U Unif(0, 1). Then U = X 3 /8, and so X = 2U 1/3 .
For U = 0.54, we get X = 1.62.
2
1
NAME
ISyE 6644 Fall 2015 Test #1 Solutions
You have 85 minutes. You get one cheat sheet. Put your succinct answers below. All
questions are 3 points, unless indicated. You get 1 point for writing your name correctly.
1. Let X be the number of tickets t