Homework 7, MATH 4410/6410
Due on Friday, April 25 (and will be counted as extra credit)
Problem 1 Ross, page 357 Problem 21.
Problem 2 Ross, page 357 Problem 22.
Problem 3 Ross, page 361 Problem 49.
Problem 4 Ross, page 361 Problem 50.
Problem 5 Ross, pa
Homework 5, MATH 4410/6410
Due on Friday, March 28
Problem 1 Suppose cfw_Xn n0 is a DTMC on the
probability matrix P is given by
0.7 0
0
0.1 0.1 0.1
0.3 0.2 0.4
P =
0
0
0
0.2 0
0
0.1 0
0
state space E = cfw_0, 1, 2, 3, 4, 5, whose transition
0 0.3 0
0
Homework 2, MATH 4410/6410
Due on Wednesday, January 29
Problem 1 Ross, pg. 173 Problem 7
Problem 2 Ross, pg. 174 Problem 15
Problem 3 Ross, pg. 175 Problem 20
Problem 4 Ross, pg. 175 Problem 21
Problem 5 Ross, pg. 177 Problem 27
Problem 6 Ross, pg. 177 P
Homework 4, MATH 4410/6410
Due on Wednesday, March 12
Problem 1 Consider a DTMC cfw_Xn n0 on a state space E = cfw_0, 1, 2, having a transition probability matrix P given by
0 0.2 0.8
P = 0.6 0 0.4
0.5 0.5 0
(a) Write down all communicating classes of th
Homework 1, MATH 4410/6410
Problem 1 Ross, pg. 16, Problem 14
Problem 2 Ross, pg. 17, Problem 21
Problem 3 Ross, pg. 18, Problem 35
Problem 4 Ross, pg. 87, Problem 8
Problem 5 Ross, pg. 87, Problem 12
Problem 6 Ross, pg. 88, Problem 25
Problem 7 Ross, pg.
Assignment for Wednesday, November 20, 2013
Do the following problems:
From Mathematics of Investment and Credit: 5.1.1 5.1.5, 5.1.8, and 5.1.12.
Submit the following problems:
1.
2.
3.
4.
5.
6.
Problem 5.1.3
Problem 5.1.4
Problem 5.1.5
Problem 5.1.8
Prob
Assignment for Wednesday, November 6, 2013
Do the following problems:
From Mathematics of Investment and Credit: 4.1.1 4.1.8, 4.1.10 4.1.12, and 4.2.1,
4.2.4 4.2.7.
Submit the following problems:
1.
2.
3.
4.
5.
6.
Problem 4.1.3
Problem 4.1.5
Problem 4.1.6
Assignment for Friday, November 1, 2013
Do the following problems:
From Mathematics of Investment and Credit: 3.2.2 3.2.9, 3.2.11, and 3.3.1 3.3.7.
Submit the following problems:
1.
2.
3.
4.
5.
6.
Problem 3.2.4
Problem 3.2.8
Problem 3.2.11
Problem 3.3.3
P
Assignment for Friday, October 4, 2013
Do the following problems:
From Mathematics of Investment and Credit: 2.2.1 2.2.7, 2.2.9 2.2.11.
Submit the following problems:
1.
2.
3.
4.
5.
Problem 2.2.3
Problem 2.2.4
Problem 2.2.6
Problem 2.2.9
Calculate the pre
Assignment for Friday, October 25, 2013
Do the following problems:
From Mathematics of Investment and Credit: 2.4.1, 2.4.4, 2.4.7, 2.4.8 (a) and (b), 3.1.1
3.1.5.
Submit the following problems:
1.
2.
3.
4.
5.
6.
Problem 2.4.1
Problem 2.4.4
Problem 2.4.8
Assignment for Friday, September 27, 2013
Do the following problems:
From Mathematics of Investment and Credit: 2.1.1, 2.1.2, 2.1.4, 2.1.14, 2.1.15, 2.1.17,
2.1.18, 2.1.19, 2.1.20, 2.1.21.
Submit the following problems:
1.
2.
3.
4.
5.
Problem 2.1.2
Proble
Assignment for Friday, October 7, 2013
Do the following problems:
From Mathematics of Investment and Credit: 2.3.1 2.3.8, 2.3.10 2.3.18.
Submit the following problems:
1.
2.
3.
4.
5.
6.
Problem 2.3.3
Problem 2.3.4
Problem 2.3.7
Problem 2.3.11
Problem 2.3.
Assignment for Wednesday, September 4, 2013
Do the following problems:
From Mathematics of Investment and Credit:
1.4.1, 1.4.2, 1.4.4, 1.4.5, 1.5.1, 1.5.4 1.5.7
Submit the following problems:
1.
2.
3.
4.
5.
Problem 1.4.2
Problem 1.4.4
Problem 1.5.1
Proble
Assignment for Wednesday, September 6, 2013
Do the following problems:
From Mathematics of Investment and Credit:
1.6.1 1.6.10
Submit the following problems:
1.
2.
3.
4.
5.
Problem 1.6.2
Problem 1.6.4
Problem 1.6.5
Problem 1.6.9
A customer is offered an i
Assignment for Wednesday, September 25, 2013
Do the following problems:
From Mathematics of Investment and Credit: 2.1.3, 2.1.5 2.1.12.
Submit the following problems:
1.
2.
3.
4.
5.
Problem 2.1.6
Problem 2.1.8
Problem 2.1.11
Problem 2.1.12
Susan and Jeff
Assignment for Wednesday, August 28, 2013
Do the following problems:
From Mathematics of Investment and Credit:
1.2.1, 1.2.3 1.2.6, 1.2.9 1.2.13.
Submit the following problems:
1.
2.
3.
4.
5.
6.
Problem 1.2.1
Problem 1.2.5
Problem 1.2.6
Problem 1.2.9
Prob
Assignment for Monday, August 26, 2013
Do the following problems:
From Mathematics of Investment and Credit:
1.1.1 1.1.12. Do not do 1.1.5(c).
Submit the following problems:
1.
2.
3.
4.
5.
Problem 1.1.1
Problem 1.1.2
Problem 1.1.6
Problem 1.1.10
An invest
Simulation Project
Due on the last week of class
This assignment is centered around learning how to simulate random variables and processes on
the computer. You are allowed to make use of whatever programming language/software you wish
to do this assignme
MATH 4410: Take-Home portion of Test 2
Instructions: This portion of the test is open-book, open notes, but you are not allowed to discuss
these problems with one another. These are due by test-time on Friday, April 11, and is worth 50
percent of Test 2.
Review of Probability Theory
We begin our review of probability theory by solving problems, whose solutions involve the use
of various concepts you should have encountered in MATH 4000.
This problem is Problem 22 of Chapter 1 of Introduction to Probabilit
MATH 4410: Take-Home portion of Test 1
Instructions: This portion of the test is open-book, open notes, but you are not allowed to discuss
these problems with one another. These are due by test-time on Wednesday, February 26, and is
worth 50 percent of Te
Comments on the Take-Home
I have received a number of questions from people in the class, so I have decided to make a
number of remarks on each Problem from the take-home, to ensure that everyones on the same
page.
Problem 1 All Im looking for here is for
Discrete-time Markov Chains
1
Introduction
We are now ready to begin our discussion of stochastic processes. The rst type of stochastic process
we will encounter is known as a Discrete-time Markov Chain, which is dened as follows.
Denition 1.1 Suppose cfw
MTHSC 4410 Simulation Project
Spring 2014
Zhongyi Zhou
April 24, 2014
1 Introduction
A discrete random variable can be simulated using a PC by first generating a uniform random
variable U on (0, 1). Since uniform random variable is evenly distributed on i
Comments on a problem in Homework 2
One of the assigned problems in Homework 2 is Problem 20 on pg. 175 of Rosss text, which
reads as follows.
Problem: An individual whose level of exposure to a certain pathogen is x will contract the disease
caused by th
Solutions to Homework 7, MATH 4410
Problem 1 The key to doing this problem is to property dene all exponential random variables
used. Let Xi,j represent the time spent by customer i at server j. All random variables are independent of one another, and all
Solutions to Homework 6, MATH 4410/6410
Problem 1
Throughout this problem, cfw_N (t); t 0 is a Poisson process with rate = 10, where N (t) = the
number of arrivals in [0, t], t being in units of hours. Here time t = 0 corresponds to 6am.
(a) The number of
Homework 6, MATH 4410/6410
Due on Monday, April 7
Problem 1 Suppose vehicles arrive to one of the I-185 toll booths outside of Greenville in accordance
to a Poisson process having rate = 10 cars per hour. Assume we arrive one morning at 6AM, and
we begin