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 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 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
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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
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ISyE 6644 Simulation Spring 2010
Professor: Dave Goldsman; Oce: Groseclose 433; Phone: 404-894-2365; email:
sman@gatech.edu; website: www.isye.gatech.edu/sman/courses/6644.
Class Times and Location: This is a Distance Learning course.
Oce Hours: Wheneve
1
ISyE 6644 Fall 2015
Homework #2 Solutions
1. Use the basic Monte Carlo technique from class to integrate
1
exp(x2 /2) dx.
I =
0
(a) Use n = 100 Unif(0,1) random variates to produce your answer. Repeat this
1000 times and make a histogram of the results.
1
NAME
ISyE 6644 Summer 2009 Test #2 Solutions
This test is open book, open notes. You have 90 minutes.
1. What does FEL mean?
Solution: Future Event List.
2
2. Suppose that U1 and U2 are PRNs. What is the expected value of 6U1 + 6U2 ?
Solution: This is
1
NAME
ISyE 6644 Summer 2009 Practice Test #2
1. True or False? You can use an Arena ASSIGN block to change the appearance of
an entity.
Solution: TRUE.
2
2. True or False? A particular Arena resource can be in more than one resource set.
Solution: TRUE.
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 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
ISyE 6644 Spring 2012
Homework #3 Solutions
1. Use the basic Monte Carlo technique from class to integrate
I=
1
1
1
expcfw_x2 /2 dx.
2
(a) Use n = 100 Unif(0,1) random variates to produce your answer. Repeat this
50 times and make a histogram of the re
1
ISyE 6644 Fall 2015
Homework #5 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 Unif(0, 1). Then U = X 4 /16, and so X = 2U 1/4 .
For U = 0.54, we get X = 1.71.
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
1
ISyE 6644 Fall 2015
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) nd X500 .
Solution: X0 = 7. Then X1 = 38 mod(16
1
NAME
ISyE 6644 Fall 2015 Test #2 Solutions
1. TRUE or FALSE? It is possible to SEIZE and RELEASE a specic member of a
resource set.
2
Solution: TRUE.
2. TRUE or FALSE? An entity attempting to reside in an Arena QUEUE block that is
already at capacity i
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
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 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 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
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 #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