STAT 571: Multivariate Statistics Homework 2
Solutions
Subhadeep Paul
September 16, 2014
1
Problem 1
The conditional p.m.f of Y given X = 2 is
(
1 exp(2) y = 0
exp(2)
y=1
Hence E(Y |X = 2) = 0 (1 exp
STAT 571 Exam: Closed book, notes, etc.
1. Suppose Z1 and Z2 are independent N (0, 1)s, and
Y1 = Z1 , Y2 = Z1 + Z2 , and Y3 = Z2 .
(a) Find the covariance matrix of the Yi s, Cov[(Y1 , Y2 , Y3 )].
Ans
Fall 2016 STAT 571 Homework 2
Solution
1. [8 pts] (Exercise 2.7.1)
(a)X A = cfw_1, 2, 3, because for each x = 1, 2, 3 there is a y with (x, y) A
(b) YxA = (0, x/2]; for each x cfw_1, 2, 3
(c) We need
Fall 2016 STAT 571 Homework 1
Solution
1. (Exercise 1.9.2)
0
(a) J n = n1 1n 1n which produces a mean vector of a colum vector. For any a =
P
0
0
0
(a1 , , an ) Rn , J n a = a
1n , where a
= n1 ni ai
STAT 571 Fall 2017 Section A1
Homework 1 Solution
1. (a)
(b) Toyota Corona and Volvo 142E
(c) Chrysler Imperial
0
2. (a) Hn 1n = (In n1 1n 1n )1n = 1n n1 1n n = 0
0
(b) According to the question, 1n x
STAT 571 Fall 2017 Section A1
Homework 3
1. [8 pts] Let
Y
= (Y1 , . . . , Yr )
where
Yj = + A + ej
2 ), the e s are N (0, 2 ), and A, e , . . . , e are all independent.
and is constant, A is N (0, A
j
Multivariate Statistics
Old School
Mathematical and methodological introduction to multivariate statistical
analytics, including linear models, principal components, covariance
structures, classificat
STAT 571 Fall 2017 Section A1
Homework 4
1. [4 pts] MSOS, Exercise 4.4.2. (Use a quadratic polynomial model. You may assume the
data are ordered such that all observations from each time period are to
STAT 571 Fall 2017 Section A1
Homework 2 Solution
1. Let X denotes the sample space/support of x. We have
X
P(X A, Y B) =
P(Y B|X = x)f (x)
xX A
Hence,
P(Y B) = P(X X , Y B)
X
=
P(Y B|X = x)f (x)
xX
=
STAT 571 Fall 2017 Section A1
Homework 5
1. [6 pts] MSOS, Exercise 5.8.4.
2. [6 pts] MSOS, Exercise 5.8.8.
3. [5 pts] Let P be any symmetric, idempotent N N matrix. From the definitions given in
lectu
STAT 571 Fall 2017 Section A1
Homework 4 Solution
1. Assume data are ordered such that all observations from each time period are together.
1 1 1
1 2 22
2
w=
1 3 3
1 4 42
1 5 52
2. (a) Since (Yb Ya
STAT 571 Fall 2017 Section A1
Homework 3 Solution
1. (a) Yj = + A + ej = + A Z0 + e Zj . Formulate this into matrix form, we can let
a = (, , . . . , )1r
.
A e 0 0
A 0 e 0
B = A 0 0 e
.
.
.
.
.
.
.
STAT 571 ~— Multivariate Analysis — Fall 2014
Exam 1
October 8, 2014
Full Name: K e?
e This is a 50 minute exam. There are 6 problems? worth a total of 48 points.
6 You may use one physical page (st
STAT 571 Exam #2: Open book & notes. Calculators are ok, but no cell phones, iPads, Kindles, Nooks,
etc.
1. Which of the following are linear subspace in R2 ? (Circle the letters for the ones that are
STAT 571 R1 (4)
Multivariate Analysis
Fall 2014
Instructor: Trevor Park, Illini Hall 115, thp2@illinois.edu
Lecture: Monday, Wednesday & Friday, 11:0011:50 AM, 156 Henry Administration Building
Instru
STAT 571 Fall 2017 Section A1
Homework 1
1. [4 pts] The data set mtcars (automatically available) has numerical features of 32
automobiles from the year 1974.
(a) Create a star plot of the first seven
STAT 571 Fall 2014 Section R1
Homework 1 Solution
1. (Exercise 1.9.1) (a) 0n , because centering 1n would just subtract the average of 1 from each
element. (b) x, because if the elements of x sum to z
STAT 571 Multivariate Analysis Fall 2015
Exam 1
October 7, 2015
Full Name:
This is a 50 minute exam. There are 5 problems, worth a total of 38 points.
You may use one physical page (standard size) o
NAME: _
STAT 571 Exam
Friday, October 11, 2013
Closed book, notes, etc.
1. Suppose Z1 and Z2 are independent N (0, 1)s, and
Y1 = Z1 , Y2 = Z1 + Z2 , and Y3 = Z2 .
(a) Find the covariance matrix of the
STAT 571 Multivariate Analysis Fall 2015
Exam 1
October 7, 2015
Full Name:
This is a 50 minute exam. There are 5 problems, worth a total of 38 points.
You may use one physical page (standard size) o
STAT 571: Multivariate Statistics Homework 3
Solutions
Subhadeep Paul
September 23, 2014
1
Problem 1
We have = 0 as the spectral decomposition of . Hence is the diagonal
matrix of the eigenvalues i a
STAT 571 m Multivariate Analysis ~ Fall 2014
Exam 2
November 19, 2014
Full Name: A 82/
a This is a 50 minute exam. There are 6 problems. worth a total of 45 points.
e You may use the textbook (Maide
STAT 571 Fall 2016
Homework 6 (due on Oct 26, 11am)
1. [4 pts] Exercise 5.8.41
2. [3 pts] Exercise 7.6.5
3. [3 pts] Exercise 7.6.6
4. [7 pts] Using the caffeine data set of Exercise 4.4.4 (available i
STAT 571 Fall 2016
Homework 7 (Due Nov 9, 2016, 11am)
1. [10 pts] (Two-Sample T 2 Test) Let Y1 (n1 q) and Y2 (n2 q) be independent, with rows
that are independent random samples from normal distributi
STAT 571 Fall 2016
Homework 2 (Due September 19, 11am)
1. [8 pts] Exercise 2.7.1
2. [4 pts] Suppose X is continuous with pdf f (x), so that
P(X A, Y B) =
P(Y B | X = x) f (x) dx
A
Suppose that, for ea
STAT 571 Fall 2016
Homework 8, due on Dec 9th, 11am
1. [3 pts] Exercise 10.5.7.
2. [9 pts] The matrix called exams has data on 191 statistics students, giving their scores (out
of 100) on three midter
Sports Data
Louis Roussos asked n = 130 people to rank seven sports,
assigning #1 to the sport they most wish to participate in, and
#7 to the one they least wish to participate in. The sports are
bas