STAT 571 HW #1: Some Answers
September 6, 2012
1
1.9.2. Jn = n 1n 1 .
n
(a) Jn a = a1n , the vector with the mean of the elements of a in each component.
(b) Jn Jn =
1
1 1 1 1 ,
n2 n n n n
1
and 1 1n = n, so Jn Jn = n 1n 1 = Jn .
n
n
(c) For the G, the rs
STAT 571 Fall 2016
Homework 1, due on Wednesday, September 7th, 11am
1. [10 pts] Exercise 1.9.2.
2. [4 pts] Exercise 1.9.3.
3. [4 pts] Exercise 1.9.10.
4. [4 pts] Exercise 1.9.11.
5. [4 pts] The data set election (in package msos) has results from the 200
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 . (b)J n J n = n12 1n 1n 1n 1n =
0
0
1
1 n1n = n1 1n 1
STAT 571 Multivariate Analysis Fall 2016
Exam 1
October 7, 2016
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) of your own personal notes and a standard
scientific cal
STAT 571 Multivariate Analysis Fall 2015
Exam 2
November 18, 2015
Full Name:
This is a 50 minute exam. There are 5 problems, worth a total of 35 points.
You may use the textbook (Marden), any personal notes (no limit), and a standard
scientific calculat
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 to sum over the three xs and integrate over y from 0 to
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 )].
Answer: You can nd the variances and covariances fairly di
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 (standard size) of your own personal notes and a standard
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.) The vectors a
and b are xed elements of R2 . The vec
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 midterm exams and a final exam. Consider a factor analysis wi
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 each x, the conditional distribution of Y given X = x is
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(2) + 1 exp(2) = exp(2)
We have,
P (Y = 1, X 1) =
=
1
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 zero, then it is already centered.
(c) Hn Hn = Hn (In n1
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) of your own personal notes and a standard
scientific cal
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 Yi s, Cov[(Y1 , Y2 , Y3 )].
1
(b) Are Y1 and Y2 indepe
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) of your own personal notes and a standard
scientific cal
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 and is an orthogonal matrix whose i th column, i is
the
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 (Maiden), any personal notes (no limit), and a standard
scien
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 in package msos), form a Y
matrix consisting of the colu
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 distributions with means 1 and 2 ,
respectively, and common inver