STOR 445
Homework 1
(Please turn in your solutions for Questions 1, 2, and 4 only.)
1. Suppose that X is a Poisson random variable with parameter 5. Let Y = min(X, 5).
Determine the following:
(a) The probability mass function of X
(b) The probability mas

STOR445 - Midterm '#1
Fall 2014
NAME: J
Please be neat and Show all your work to get partial credit. W’rite your name on each page.
GOOD LUCK.
Question 1:
Question 2:
Question 3:
Question 4:
Total: NAME:
1 Let X be a continuous random variable with probab

STOR 445 FINAL SOLUTION
Saturday, Dec 7, 2013.
12:00-2:15pm.
1. Attempt all problems. Show all work.
2. All sub-problems carry 5 points.
3. The exam is open book, open notes.
4. Laptops, calculators are allowed.
5. No communication about the exam is allow

STOR 445 MIDTERM II
Tuesday, Oct 29, 2013.
2:00-3:15pm.
1. Attempt all problems. Show all work.
2. The problem weights are as given in the parentheses.
3. The exam is open book, open notes.
4. Laptops, calculators are allowed.
5. No communication about th

STOR 445 MIDTERM I
Thursday, Sept 19, 2013.
2:00-3:15pm.
1. Attempt all problems. Show all work.
2. The problem weights are as given in the parentheses.
3. The exam is open book, open notes.
4. Laptops, calculators are allowed.
5. No communication about t

Solutions to exercises: week 6
Concep. 6.20 Consider the queue in front of server 1. The inter-arrival times are iid,
each being a sum of two iid exp() random variables. Hence it is a
G/M/1 queue.
Concep. 6.21 The pdf of an U(a, b) random variable is
1
,

Solutions to exercises: week 1
Concep. 2.8 We have
Xn+1
1
2
=
2
0
with
with
with
with
probability
probability
probability
probability
1, if Xn = 0
1, if Xn = 1
p, if Xn = 2
1 p, if Xn = 2.
Since Xn+1 depends only on the current state and not on the past,

STOR 445, Fall 2013
Practice Questions for MT1
Question 1)
Jobs in a manufacturing shop need to go through two tasks: Task 1 and Task 2. There
are two workers in this shop. Worker 1 is responsible for Task 1 and Worker 2 is responsible
for Task 2. Each jo

Probabilities
Conditional probability
Independence
Binomial coefficient
Theorem of total probability
a partition
Bayes' Rule
Indicator Function
Important Discrete Random Variables
Expected value
Probability Mass Function
Conditional Probability Mass Funct

STOR 445 MIDTERM I
Thursday, Sept 24, 2015.
9:30-10:45am.
1. Attempt all problems. Show all work.
2. The problem weights are as given in the parentheses.
3. The exam is open book, open notes.
4. Laptops, calculators are allowed.
5. No communication about

STOR 445
Homework 2
1. Suppose that the demand for a particular t-shirt the UNC Student Stores sells is
deterministic with 50 units per month. Each t-shirt costs $10 and the monthly charge
of carrrying one dollar worth of the inventory is 50 cents. If the

HW #7 Solutions
Computational Problems
3.8 The number of miles until first failure is the minimum of four iid Exp(1/5000) random
variables, the remaining number of miles until second failure is, by the strong memoryless
property, the minimum of an Exp(1/1

*
*
*
*
MAXIM
*
*
*
*
1. Introduction
MAXIM is a collection of MATLAB programs (m-files) intended to be used with the
book `Introduction to Modeling and Analysis of Stochastic Systems (Second Edition)'
by V G Kulkarni. These files were created by using MA

Lifetime Fitness Final Exam Review
The LFIT final will be given on Sakai
Come to Fetzer Gym A on the LAST day of class during your regular class time.
Bring your computer and make sure your battery is fully charged before the exam (no outlets will
be avai

Heteroscedasticity
1. Nature of Heteroscedasticity
Heteroscedasticity refers to unequal variances of the error i for different observations. It may be
visually revealed by a "funnel shape" in the plot of the residuals ei against the estimates Yi or
agains

STOR 445
Final Exam
This test consists of 5 questions on 3 pages.
The duration of the exam is 2.5 hours.
The exam is closed book and notes but you can use a letter-sized
reference sheet (one side only).
Calculators and cell phones are not allowed.
Wr

STOR 445
Midterm Exam 2
November 15, 2012
This test consists of 3 questions on 2 pages.
The exam is closed book and notes.
Calculators and cell phones are not allowed.
Write your name on this question sheet and your blue book.
Please return them both.

HW #8 Solutions
1 a. X(t) = the number of calls in the
0
0
R=
0
0
0
system at time t. The state space is cfw_0, 1, 2, 3, 4, 5.
0 0 0 0
0 0 0 0
2 0 0 0
.
0 3 0 0
0
3 0
0 0 0 3 0
b. = 2 per hour and
P = 4 per hour. Expected number of busy agents a

Solutions to exercises: week 5
Concep. 5.1 Let the successive lifetimes of the batteries in the replacement problem
of Example 5.2 be Li . Define N0 = 0 and define
Nr+1 = mincfw_i > Nr : Li > 3, r 0.
Thus the Nr th replacement is the rth planned replaceme

STOR 445 MIDTERM I
Thursday, Sept 19, 2013.
2:00-3:15pm.
1. Attempt all problems. Show all work.
2. The problem weights are as given in the parentheses.
3. The exam is open book, open notes.
4. Laptops, calculators are allowed.
5. No communication about t

Diagnostics & Remedies in Simple Regression
1. Residual Analysis & the Healthy Regression
1. Residual Plot of the Healthy Regression
Residual analysis is a set of diagnostic methods for investigating the appropriateness of a
regression model based on the

Matrix Representation of the Regression Model
1. Introduction to Matrices
These notes cover the following:
1. properties of, and operations on, matrices and vectors
2. matrix representation of the linear regression model, both simple and multiple
3. deriv

Multiple Linear Regression
1. The Multiple Regression Model in General
1. Multiple Regression Model with p - 1 Independent Variables
The multiple linear regression model with p - 1 independent variables can be written
Yi = 0 + 1 Xi,1 + 2 Xi,2 + + p-1 Xi,p

Outlying & Influential Observations
1. Added-Variable Plots for Functional Form & Outlying Observations
1. Uses of Added-Variable Plots
Added-variables plots are also called partial regression plots and adjusted variable plots.
A partial regression plots

Polynomial Regression & Interactions
1. Polynomial Regression with One Predictor Variable
1. Formulation of the Model
A nonlinear relationship between y and x can often be approximately represented within the
general linear model as a polynomial function