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 original position. If it goes left,
then with probability 1
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
Interchange the order of summation.
j 1
Pcfw_N j Pcfw_N j j * Pc
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
E[ X ] F ( x)dx where F ( x) 1 F ( x) Pcfw_X x
0
2. If
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 position. If it goes left,
then with probability 1/3 it will
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
policy is exponentially distributed with mean $2000, what
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 money paid on each
policy is exponentially distributed
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 accessible is n or fewer steps.
3. Discuss why a finite state Ma