IE:3610 Stochastic Modeling (Fall 2015)
Homework 1
Solutions
1. Problem 24-1 (a, b) from Chapter 24 (on ICON)
A cube has its six sides colored red, white, blue, green, yellow, and
violet. It is assumed that these six sides are equally likely to show
when
IE:3610 Stochastic Modeling (Fall 2015)
Homework 1
due Thursday, Sep 3, at the beginning of the class
1. Problem 24-1 (a, b) from Chapter 24 (on ICON)
2. Problem 24-2 (c) from Chapter 24 (on ICON)
3. Problem 24-3 (ad) from Chapter 24 (on ICON)
4. A fair c
IE:3610 Stochastic Modeling (Fall 2015)
Homework 2
Solutions
HW2 (due Thu, Sep 10): 24-4(a,b,c); 24.5; 24-8(a-d); 24-9(a,b,c); 24.13.
24-4 (a, b, c) The random variable X has density function f given
by
8
>
<
fX (y) = K
>
:0
for 0 y
for < y 1
elsewhere
(
IE:3610 Stochastic Modeling (Fall 2015)
Homework 13
Solutions
HW13 (not graded): 15.2-3; 15.2-4; 15.2-5; 15.4-2.
15.2-3
Consider the game having the following payoff table:
P layer1 1
P layer1 2
P layer1 3
P layer2 1
2
-1
-1
Table 1: 15.2-3 Data
P layer2
Stochastic Modeling
Associate Prof. Amaury Lendasse
IE:3610
Who am I?
Belgian: sorry for my
french accent :)
2
Who am I?
Belgian: sorry for my
french accent :)
Bachelor and Masters in
Mechanical Engineering
Masters in Control
3
Who am I?
Belgian: sor
IE:3610 Stochastic Modeling (Fall 2015)
Homework 5 (due Thu, Oct 1)
Solutions
HW5 (due Thu, Oct 1): 29.2-1(a); 29.2-2(a); 29.3-1(a,b) 29.3-2(a,b);
29.3-3(a,b), 29.4-2, 29.4-5.
29.2-1(a)
Solution:
(a) Since the probability of rain tomorrow is only dependen
Q=
31622.78
(optimal order quantity)
The results are the same as those in (c).
(e)
U
#OH
2
#!"!
!%
$" '#() gallons purchased with each order
18.3-5.
(a) U will decrease by half.
(b) U will double.
IE:3610 Stochastic Modeling (Fall 2015)
(c) U remainsHom
IE:3610 Stochastic Modeling (Fall 2015)
Homework 8 (due Thu, Oct 29)
Solutions
HW8 (Due Thu, OCT 29): 17.6-3; 17.6-10 (a,c,e); 17.6-12; 17.6-15.
17.6-3
Solution:
M/M/1 model
Proportion of time no one is waiting to be served =
= P (number of customers in t
Stochastic Modeling
Associate Prof. Amaury Lendasse
IE:3610
Text?
F. S. Hillier and G. J. Lieberman, Introduction to Operations
Research, McGraw-Hill, 10th edition (2015), 1047 pp. ISBN:
9781259162985
2
Class topics
Review of probability
Decision under un
Stochastic Modeling
Associate Prof. Amaury Lendasse
IE:3610
Text?
F. S. Hillier and G. J. Lieberman, Introduction to Operations
Research, McGraw-Hill, 10th edition (2015), 1047 pp. ISBN:
9781259162985
2
Class topics
Review of probability
Decision under un
056:166 Stochastic Modeling
Homework 2
Solutions
24-4 (a, b, c) The random variable X has density function f given
by
fX (y) = K
0
for 0 y
for < y 1
elsewhere
(a) Determine K in terms of .
(b) Find FX (b), the CDF of X.
(c) Find E(X).
Solution:
(a) By th
Stochastic Modeling
Associate Prof. Amaury Lendasse
IE:3610
Text?
F. S. Hillier and G. J. Lieberman, Introduction to Operations
Research, McGraw-Hill, 10th edition (2015), 1047 pp. ISBN:
9781259162985
2
What is modeling?
In this class, you will learn how
Stochastic Modeling
Associate Prof. Amaury Lendasse
IE:3610
Text?
F. S. Hillier and G. J. Lieberman, Introduction to Operations
Research, McGraw-Hill, 10th edition (2015), 1047 pp. ISBN:
9781259162985
2
What is modeling?
In this class, you will learn how
Stochastic Modeling
Associate Prof. Amaury Lendasse
IE:3610
Text?
F. S. Hillier and G. J. Lieberman, Introduction to Operations
Research, McGraw-Hill, 10th edition (2015), 1047 pp. ISBN:
9781259162985
2
What is modeling?
In this class, you will learn how
Stochastic Modeling
Associate Prof. Amaury Lendasse
IE:3610
Text?
F. S. Hillier and G. J. Lieberman, Introduction to Operations
Research, McGraw-Hill, 10th edition (2015), 1047 pp. ISBN:
9781259162985
2
Stochastic Modeling
Assignments:
Homework
Quizzes
29.8-1.
(a)
(b) Steady-state equations:
(c) Solving the steady-state equations gives
.
29.8-2.
(a) Let the state be the number of jobs at the work center.
(b) Steady-state equations:
(c) Solving the steady-state equations gives
29-11
.
IE:3610 Stochastic Modeling (Fall 2014)
Homework 9 (due Thu, Nov 6)
Solutions
HW9 (Due Thu, Nov 6): 17.6-3; 17.6-10 (a,c,e); 17.6-11; 17.6-12; 17.6-15.
17.6-3
Solution:
M/M/1 model
Proportion of time no one is waiting to be served =
= P (number of custome
IE:3610 Stochastic Modeling (Fall 2014)
Homework 5 (due Thu, Oct 9)
Solutions
HW5 (due Thu, Oct 9): 29.2-1(a); 29.2-2(a); 29.3-1(a,b) 29.3-2(a,b);
29.3-3(a,b).
29.2-1(a)
Assume that the probability of rain tomorrow is 0.5 if it is raining
today, and assum
IE:3610 Stochastic Modeling (Fall 2014)
Homework 7 (due Tuesday, Oct 21)
Solutions
HW7 (Due TUESDAY, OCT 21): 29.6-1; 29.6-2; 29.7-1(a,c); 29.7-2.
29.6-1
A computer is inspected at the end of every hour. It is found to be
either working (up) or failed (do
IE:3610 Stochastic Modeling (Fall 2014)
Homework 6 (due Thu, Oct 16)
Solutions
HW6 (due Thu, Oct 16): 29.4-2; 29.5-4; 29.5-5; 29.5-8; 29.5-9.
29.4-2
Given each of the following (one-step) transition matrices of a Markov
chain, determine the classes of the
056:166 Stochastic Modeling (Fall 2013)
Homework 1
Solutions
1. Problem 24-1 (a, b) from Chapter 24 (on ICON)
A cube has its six sides colored red, white, blue, green, yellow, and
violet. It is assumed that these six sides are equally likely to show
when
IE:3610 Stochastic Modeling (Fall 2014)
Homework 10 (Due Thu, Nov 13)
Solutions
HW10 (Due Thu, Nov 13): 17.6-26; 17.6-29; 17.6-30; 17.7-5; 17.7-6.
17.6-26
Solution:
These form M/M/1/K queues with K = 1,3 and 5 respectively, = 1/4
and = 1/3, so = 3/4 and t