29.09.2014
IE 450  PS I
1. Each morning an individual leaves his house and goes for a run. He is equally likely to leave either from his
front or back door. Upon leaving the house, he chooses a pair of running shoes (or goes running barefoot if
there are
20.10.2014
IE 450  PS 3
1.
A problem of interest to sociologists is to determine the proportion of society that has an upper or lowerclass occupation. One possible mathematical model would be to assume that transitions between social
classes of the succ
PS3
~)
1
01
\\e 1\
\
(I
(I
I
bS;iCG
1)\),
'I
o
II
\1;\
o, LnJ1
(
\J,)
\J
"
1
.,.
A
,
'\
rr~,U~l'>
OIL\J1 ':.: 0 1
I
I"'"
1
1
0,
\)1
1
<
)
[J,
f
\11
1 rOll1
.3 L,.
\
01 1
1
(J/ i l
\'
\)JI', \
\
I
,
1
SIT\
Ce
c
,;?
.
~
)
I
!'c.A._
we
(
<;
(
(~"O/Y~
6"
\
08.10.2014
IE 450 PS 2
1. At all times, an urn contains N ballssome white balls and some black balls. At each
stage, a coin having probability p of landing heads is flipped. If heads appears, then a
ball is chosen at random from the urn and is replaced by
13.10.2014
IE 450 QUIZ 1
Name:
Surname:
ID:
1. (35%) Coin 1 comes up heads with probability 0.6 and coin 2 with probability 0.5. A
coin is continually flipped until it comes up tails, at which time that coin is put aside
and we start flipping the other on
IE 450
Syllabus
Boazii University
Department of Industrial Engineering
Korugan
Fall 2014
Stochastic Models in Operations Research
The objective of this course is to give an intermediate level of understanding in modeling and
optimization of systems presen
05.11.2014
IE 450 PS 5
1. Show that if cfw_Ni(t), t 0 are independent Poisson processes with rate i , i = 1, 2, then cfw_N(t), t0
is a Poisson process with rate 1 + 2 where N(t) = N1(t) + N2(t).
2. Let cfw_N(t), t 0 be a Poisson process with rate . Let Sn
03.11.2014
IE 450  PS 4
1.
Consider a branching process having < 1. Show that if X0 = 1, then the expected number of
individuals that ever exist in this population is given by 1/(1)? What if X0= n?
2. Consider a branching process where P0 = 1/4, P1 = 1/4
PS
f
f(
N1 (I )f
c"~';:J;cfw_> (  ~" P(
~)/ltc\)
7
NcJ () ><
I
')
l(! N,iI) J) . f I IV,
NlI) i Ill" ll)
WI
PI N/I
.
r:JD

e
'>1
x
(
) .
X~'j
~1
)'14'\ )1)
e_
..
f)
f? tv ll) I :
:;<
2)
t~
tt)
~d/
'.7f/C
o
. C
'", .
)
_e._._". _._ ._.".".
._
._