Michael H. Kutner
Christopher J. Nachtsheim
University of Minnesota
University of Georgia
1. Estimate the model
Yt = a0 + a1t + a2t2 + 1u1t + 2u2t + d-1ud-1,t + t,
where t ~ WN(0,2) and ujt, j=1,d-1 are seasonal indicator variables using the data set UKDriverDeaths.
Using F test,
Homework 4 Solutions for W4437
Due on Feb 22nd, 2014
88 points in total.
2.14: (12 points)
Xt = A cos(wt) + B sin(wt),
A,B uncorrelated (0,1).
(a) P1 X2 = 11 X1 where (0)11 = (1) 11 = (1) = cos w, hence we have
P1 X2 = cos wX1
E(X2 P1 X2 )2 = (0) 11 (
Homework 2 Solutions for W4437
Due on Feb 8th, 2014
70 points in total.
1.3: (8 points)
EXt is independent of t since Xt is strictly stationary and EXt exists.
E(Xt+h Xt ) is independent of t since the joint distribution of Xt+h and Xt is independent of t
Time Series Analysis (STAT 758) Fall 2006 Homework 1 Example Solution
Written by: Fares Qeadan, Reviewed by: Ilya Zaliapin Department of Mathematics and Statistics, University of Nevada, Reno Ex(1.1) :
By denition, a stochastic process Xt is strictly stat
Solutions to selected problems in
Brockwell and Davis
This document contains solutions to selected problems in
Peter J. Brockwell and Richard A. Davis, Introduction to Time Series and Forecasting, 2nd Edition, Springe
Baye's Theorem shows how to revise a prior probability to obtain a conditional or posterior probability
when another event's occurrence is known.
A company is producing two types of ski goggles. Thirty percent of the p
STAT 587 Homework Assignment No.1 Problem 2 A. Brand preference. In a small-scale experimental study of the relation between degree of brand liking (Y ) and moisture content ( X 1 ) and sweetness ( X 2 ) of the product, the following results were obtained
Bayes Theorem Examples
A company is producing two types of ski goggles. Thirty-percent of
the production is of type A, and the rest is of type B. Five percent of
all type A goggles are returned within 10 days after the sale
Model 1 is a uniform distribution from 0 to 100. Determine the table entries for a
generalized uniform distribution covering the range from a to b where a < b.
Let X be a discrete random variable with probabilit
BASKIN SCHOOL OF ENGINEERING
Department of Applied Mathematics
AMS 132/206 Winter 2012
To be handed by Tuesday Jan 24, 2012 at the end of the class.
Please show your work in all the problems. AMS 132 students should hand in
Provide detailed steps in arriving at the solution to each of the following problems.
An investor purchases a call option with an exercise price of $55 for $2.60. The same investor
sells a call on the same security with an exercise price of $60
CUH 2013 RESEARCH PROJECT - GASB45 Report Research Project - Student Assignments (5 States)
Each Student is Assigned 5 States and the goal is to find a total of 3 reports per Student in their combined 5 states (e.g., you can find
Syllabus: Course C / Actuarial Models
Name: Basil Rabinowitz
Classes start and end date: 9/3/2013 12/3/2013
Location: C03 School of Social Work
1. Course Overview
This course provides an introduction to modeling and covers important actuarial methods that
Homework 3 Solutions for W4437
Due on Feb 15th, 2014
90 points in total.
2.1: (10 points)
We nd the best linear predictor Xn+h = aXn +b of Xn+h by nding a and b such that E(Xn+h Xn+h ) = 0
n+h )Xn ] = 0. We have
and E[(Xn+h X
E(Xn+h Xn+h ) = E(Xn+h ) aEX
Homework 5 Solutions for W4437
Due on March 1st, 2014
70 points in total.
3.5: (12 points)
Yt = Xt + Wt
EYt = 0
Cov(Yt+h , Yt ) = Cov(Xt+h + Wt+h , Xt + Wt )
= X (h) + W (h)
(since cfw_Xt cfw_Wt )
X (h) + W
if h = 0
So EYt and Cov(
Does running shod versus barefoot affect lower extremity biomechanics, kinetics, and kinematics, and
what influence do these conditions have on likelihood of injury?
Since the 1970s and the introduction of the modern day running shoe, runnin
Solution of Assignment 2
a. The process Xt = Zt + 0.3Zt1 0.4Zt2 where Zt W N (0, 1) is stationary. Note that
X (t) = E[Xt ] = 0;
X (h) = Cov(Xt+h ; Xt ) = Cov(Zt+h + 0.3Zt+h1 0.4Zt+h2 ; Zt + 0.3Zt1 0.4Zt2 )
1.25 if h = 0
0.18 if |h| = 1
a. Since Zt and Wt are uncorrelated, then so are Xt and Wt and hence Yt is stationary (see
assignment 1) and
Y (h) = X (h) + w (h) =
+ w if h = 0,
|h| , elsewhere.
b. Let h 2.
E(Ut Ut+h ) = E[(Yt Yt1 )(Yt+h Yt+
Statistics 108 Instructor: Prabir Burman
Sample MIDTERM II SHOW ALL WORK
The marketing director of a major softwood timber products company has developed a model to predict monthly lumber orders from her firm's domestic markets. Data were collected for th
Solution for Homework 1
January 15, 2009
a. Y =168.600000+2.034375X
b. Yh =249.975
c. 1 =2.034375
Simple Linear Regression Practice
1. Match each correlation with its possible scatterplot. Note all scatterplots will not be
2. The director of admissions of a small college selected 120 students at random from the