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
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
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 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
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 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 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
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
.
Melissa Ambrosch
L.J. Kuhlman
Interpretation of Literature
10/16/2015
I forced the last stone into its position; I plastered it up. Against the new masonry I
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pa
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L.J. Kuhlman
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L.J. Kuhlman
Interpretation of Literature
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1
Melissa Ambrosch
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Personal Media History Paper
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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
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
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