IE 522 Homework Assignment #1
1. Let N denote a non-negative integer-valued random variable. Show that
k 1
k 0
E[ N ] Pcfw_N k Pcfw_N k
If X is continuous with distribution function F, then show that
IE 522 Homework Assignment #4.
1. Review problems 6 and 7 from Homework #3.
2. Show that if the number of states in a Markov chain is n, and if state j is accessible
from state i, then it is accessibl
IE 522 Homework Assignment #1 Solutions.
1. Let N denote a non-negative integer-valued random variable. Show that
k 1
k 0
E[ N ] Pcfw_N k Pcfw_N k
Solution:
Pcfw_N k Pcfw_N j
k 0
k 0 j k 1
Interchang
IE 522 Homework Assignment #2
1. A rat is trapped in a maze. Initially it can choose one of two directions. If it goes right,
then it will wander around for 3 minutes and return to its original positi
IE 522 Homework Assignment #2 Solutions.
1. A rat is trapped in a maze. Initially it can choose one of two directions. If it goes right,
then it will wander around for 3 minutes and return to its orig
4.18. Jobs arrive at a precessing center in accordance with a Poisson process
with rate A. However, the center has waiting space for only N jobs and
so an arriving job nding N others waiting goes away
IE 522 Homework Assignment #3 - (All problems from Ross)
1. An insurance company pays out claims on its life insurance policies in accordance with
a Poisson process having rate 5 per week. If the amou
IE 522 Homework #4 Solutions
6. A transition probability matrix P is said to be doubly stochastic if
p
ij
= 1 for all j
i
(all column sums equal one). If a doubly stochastic chain has n states, a sing
IE 522 Homework #3 Solutions
1. An insurance company pays out claims on its life insurance policies in accordance with
a Poisson process having rate 5 per week. If the amount of money paid on each
pol
IE 522 Homework #5 Solutions.
1. A repair facility, which restricts the number of jobs in the shop to two, gives priority to
some types of jobs. If a priority job arrives while the mechanic (there is
IE 522: Industrial Systems Optimization II Fall 2015.
Midterm Exam, November 2, 2015
Name: _
Possible
I.
Conditional Expectation
45
II. Poisson Process
35
III. Markov Chains
20
Total possible
1
100
Sc
IE 522 Homework Assignment #5.
1. A repair facility, which restricts the number of jobs in the shop to two, gives priority to
some types of jobs. If a priority job arrives while the mechanic (there is
IE 522 Homework Assignment #4.
From HW #3
6. A transition probability matrix P is said to be doubly stochastic if
p
ij
= 1 for all j
i
(all column sums equal one). If a doubly stochastic chain has n s
IE 522 Homework #3 Solutions
1. An insurance company pays out claims on its life insurance policies in accordance with
a Poisson process having rate = 5 per week. If the amount of money paid on each
p
IE 522 Homework Assignment #1
1. (Ross) Let N denote a non-negative integer-valued random variable. Show that
k =1
k =0
E[ N ] = Pcfw_N k = Pcfw_N > k
If X is continuous and non-negative with distribu
IE 522 Homework Assignment #3 Not to be turned in.
1. An insurance company pays out claims on its life insurance policies in accordance with
a Poisson process having rate 5 per week. If the amount of
IE 522 Homework Assignment #2 Solutions.
1. A rat is trapped in a maze. Initially it can choose one of two directions. If it goes right,
then it will wander around for 3 minutes and return to its orig