IE 336
Aug. 31, 2012
Handout #2
Due Sep. 7, 2012
Homework Set #1
1. Let B1 , B2 , . . . , Bn be a partition of the sample space of a random experiment. Using
the axioms 1 3 show that
n
P (A) =
P (A|Bi
Homework Set #1 Solutions
IE 336 Spring 2012
1. Let S denote the sample space. If events Bi partition the sample space, then:
S = B1 B2 Bn If A is an event from the sample space, then A can also be ex
Homework Set #2 Solutions
IE 336
Fall 2012
1. (a) Let X equal number of good chips that appear. Then, X Binomial(n, p), where n > 1000
and p = 2/5. Since n is suciently large, the binomial distributio
IE 336
Sep. 7, 2012
Handout #3
Due Sep. 14, 2012
Homework Set #2
1. Consider a group of n (say n > 1000) chips. Each chip in the group can be either good
2
or bad. Assume that each of the chips is goo
Homework Set #2 Solutions
IE 336
Fall 2014
1. (a) Let X equal number of good chips that appear. Then, X Binomial(n, p), where n > 1000
and p = 2/5. Since n is suciently large, the binomial distributio
PURDUE UNIVERSITY,
IE 336
Homework Problem 2
Solutions
September 8, 2015
1 P ROBLEM : T RANSLATE R AW D ATA INTO T RANSITION M ATRIX
A market survey has been conducted to determine the movements of pe
Homework Set #1 Solutions
IE 336 Spring 2011
1. Let S denote the sample space. If events Bi partition the sample space, then:
S = B1 B2 Bn If A is an event from the sample space, then A can also be ex
IE 336 Jan. 21, 2011
Handout #2 Due Jan. 28, 2011
Homework Set #1
1. Let B1 , B2 , . . . , Bn be a partition of the sample space of a random experiment. Using the axioms 1 3 show that
n
P (A) =
i=1
P
Homework Set #2 Solutions
IE 336 Spring 2012
1. (a) Let X equal number of good chips that appear. Then, X Binomial(n, p), where n > 1000 and p = 2/5. Since n is sufficiently large, the binomial distri
PURDUE UNIVERSITY,
IE 336
Test 2
2015/10/15
Name
PUID
Test time: 1 Hour
Test Score: 20 points
Total Problems: 4
1
1 P ROBLEM O NE
Considering a businessman who keeps traveling between West-Lafayette a
Homework Set #3 Solutions
IE 336
Fall 2014
1. From HW1, we know that fX (x) = 2ex 2e2x , 0 x < and fY (y) = 2e2y , 0 y < .
Determine E(Y ): Y exp(2). Therefore, E(Y ) =
1
= 1.
2
Determine E(X):
E (X)
IE 336
Feb. 1, 2013
Handout #4
Due Feb. 8, 2013
Homework Set #3
1. As in problem 4 from homework 1, let f (x, y ) = 2exy , 0 y x < be the joint pdf of
two random variables X and Y . Find E (Y ), E (X
Homework Set #3 Solutions
IE 336 Spring 2011
1. From HW1, we know that fX (x) = 2ex 2e2x , 0 x < and fY (y ) = 2e2y , 0 y < . Determine E (Y ): Y exp(2). Therefore, E (Y ) = Determine E (X ): E (X ) =
Homework Set #1 Solutions
IE 336
Fall 2012
1. Let S denote the sample space. If events Bi partition the sample space, then:
S = B1 B2 Bn
If A is an event from the sample space, then A can also be expr
Homework Set #3 Solutions
IE 336 Spring 2012
1. From HW1, we know that fX (x) = 2ex - 2e-2x , 0 x < and fY (y) = 2e-2y , 0 y < . Determine E(Y ): Y exp(2). Therefore, E(Y ) = Determine E(X): E (X) = =
PURDUE UNIVERSITY,
IE 336
Homework Problem 2
Solutions
September 16, 2015
1 P ROBLEM : T RANSLATE R AW D ATA INTO T RANSITION M ATRIX
A market survey has been conducted to determine the movements of p
IE 33600: Operations Research Stochastic Models (Fall 2015)
School of Industrial Engineering, Purdue University
Instructor: Prof Joaqun Goi ([email protected])
initially Prof. Vaneet Aggarwal (vanee
.9"
70 8.
Chapter 2
I
Formulating Markov Chain Models
about the U. S. automobile manufacturers are concemedin lon of foreign cars in the domestic market' Chrysler' Iornp",l
oarticular'seemstovrewltssu
IE 336: Operations Research - Stochastic Models
Exam #2
Solutions
Spring 2008
1. Assume that there is a group of people on vacation in some tropical climate. In the morning of any
given day of vacatio
Homework Set #4 Solutions
IE 336
Spring 2012
1. (a) Let cfw_1, 2, 3 represent the states of the Markov chain.
Figure 1: Transition Diagram for Problem 1a
(b) Determine p, q , and r.
2r + 3p +
q
3
=
=
Homework Set #5 Solutions
IE 336
Fall 2012
1. (a) p, q , and r can be determined by solving the matrix form of the system of equations:
1
2
2
p
1
2 4/3 4/3 q = 1
1/2
1
3
r
1
Solving yields p = 1/4,
Homework Set #3 Solutions
IE 336
Spring 2012
1. From HW1, we know that fX (x) = 2ex 2e2x , 0 x < and fY (y ) = 2e2y , 0 y < .
Determine E (Y ): Y exp(2). Therefore, E (Y ) =
1
= 1.
2
Determine E (X ):
IE 336
Feb. 29, 2008
Name:
Test #1
1. Let
f (x, y ) =
4(xy +y 2 )
55
0 x 3, 1 y 2
otherwise
0
be the joint pdf of two continuous random variables X and Y .
(a) Compute f (y |x).
(b) Compute E (Y |x).
IE 336
May 8, 2009
Name:
Final Exam
1. Assume that the transition diagram of discrete Markov chain X is as given on gure below. If the
process is at some point in state 1 the probability that it will
IE 336
December 20, 2008
Name:
Final Exam
1. Assume that the transition diagram of a discrete Markov chain X is as given on gure below.
p+q
2p
2q
4
p
3
1
3p
0.7
2q
q
p
5
0.3
2
(a) Compute p and q . De