Stochastic Models
IE 5532, University of Minnesota, Fall 2016
Instructor:
William L. Cooper
Office: ME 130F
Phone: (612) 624-4322
Email: billcoop@umn.edu
Office Hours:
Mondays 11:00 AM 12:00 PM
or by appointment
Meeting Time, Location:
Tuesdays and Thursd

IE 5532 Homework #4
Due: 1:30 PM October 27, 2016.
When completing this homework assignment, you may choose to work in a group with at most two
other students. On your write-up, please indicate with whom you worked (if anyone). You must
write your own ass

IE 5532 Homework #2 Selected Solutions
1. For i = 1, . . . , r, k = 1, . . . , n let
1
Ii,k =
0
Note that Ni =
(i) ENi = E
if outcome i occurs on trial k
otherwise.
n
k=1 Ii,k .
n
k=1 Ii,k
=
n
k=1 EIi,k
n
=
k=1 pi = npi .
n
n
(ii) Var(Ni ) = Var( k=1 Ii

IE 5532 Homework #1
Due: 1:30 PM, September 27, 2016.
When completing this homework assignment, you may choose to work in a group with at most two
other students. On your write-up, please indicate with whom you worked (if anyone). You must
write your own

IE 5532 Homework #1 Selected Solutions
3. Solution to problem 46(a), chapter 2.
Following the hint in the book, let In = 1(X n) for n = 1, 2, . . . . Then X =
EX = E
In =
n=1
EIn =
n=1
P (In = 1) =
n=1
P (X n) =
n=1
n=1 In ,
and
P (X > n) .
n=0
For a dier

IE 5532 Homework #3
Due: 1:30 PM, October 20, 2016.
When completing this homework assignment, you may choose to work in a group with at most two
other students. On your write-up, please indicate with whom you worked (if anyone). You must
write your own as

IE 5532 Homework #2
Due: 1:30 PM, October 11, 2016.
When completing this homework assignment, you may choose to work in a group with at most two
other students. On your write-up, please indicate with whom you worked (if anyone). You must
write your own as