Stat 217, Winter 2012, Midterm Solutions
February 14, 2012
(Prepared by Stefan Wager)
Question 1
(a) Each row sum is 1 Its stochastic. Column 1 doesnt sum to 1 its
not doubly stochastic.
(b)
(3) (2, 4) = 0.6 (2) (3, 4)
= 0.6 (0.6 (1) (4, 4) + 0.1 (1) (5,
Statistics 202:
Data Mining
c Jonathan
Taylor
Statistics 202: Data Mining
Week 5
Based in part on slides from textbook, slides of Susan Holmes
c Jonathan Taylor
October 29, 2012
1/1
Statistics 202:
Data Mining
c Jonathan
Taylor
Part I
Linear Discriminant
STATS 217, Winter 2013, Midterm
February 12, 2013
Write your name and sign the Honor code in the blue books provided.
Please write your name on this question paper and hand it back together with your answer
booklet. This is an open material exam. You have
Statistics 305
Homework 1, due Thursday, October 4, 2012
by 5pm.
This problem set is partly aimed at getting you going with R. The coursework
webpage points you to a useful R primer (in the supplementary materials); the
rst few chapters of Dalgaard Introd
Introduction to Stochastic Processes
Stat217, Winter 2012
Homework 4 - due at 5:00 pm on Friday, February 10, 2012
TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edition.
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th e
Introduction to Stochastic Processes
Stat217, Winter 2013
Homework 1 - due at 5:00pm on Friday January 18, 2013
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd e
Stat 217 Final Examination - Winter 2012
March 22, 2012
Write your name and sign the Honor code in the blue books provided.
This is an open material exam. You have three hours to solve all four questions, each worth
points as marked (maximum of 100). Comp
Introduction to Stochastic Processes
Stats 217, Winter 2015
Homework 1 - due on Friday January 16, 2015
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edition)
Introduction to Stochastic Processes
Stat217, Winter 2013
Homework 4 - due at 11:00am on Friday February 08, 2013
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd
Introduction to Stochastic Processes
Stats 217, Winter 2015
Homework 3 - due on Friday January 30, 2015
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edition)
Introduction to Stochastic Processes
Stats 217, Winter 2015
Homework 2 - due on Friday January 23, 2015
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edition)
Introduction to Stochastic Processes
Stat217, Winter 2013
Homework 2 - due at 5pm on Friday January 25, 2013
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edit
Introduction to Stochastic Processes
Stat217, Winter 2013
Homework 1 - due at 5:00pm on Friday January 18, 2013
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd e
STATS 217, Winter 2013, Midterm
February 12, 2013
Write your name and sign the Honor code in the blue books provided.
Please write your name on this question paper and hand it back together with your
answer booklet. This is an open material exam. You have
Introduction to Stochastic Processes
Stat217, Winter 2012
Homework 1 - due at 5:00pm on Friday January 20, 2012
TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edition (or Pinsky and
Karlin, 4th edition)
1. Problem III.1.1 on page 99 of T
Introduction to Stochastic Processes
Stat217, Winter 2013
Homework 2 - due at 5:00pm on Friday January 25, 2013
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd e
Introduction to Stochastic Processes
Stat217, Winter 2012
Homework 2 - due at 5 pm on Friday, January 27, 2012
TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edition.
1. Problem III.4.3 on page 130 of TK.
2. Problem III.4.4 on page 131 o
Introduction to Stochastic Processes
Stat217, Winter 2013
Homework 3 - due at 11:00 am on Friday Feb 01, 2013
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edi
Introduction to Stochastic Processes
Stat217, Winter 2013
Homework 8
TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edition.
1. Problem VI.4.1 on page 377 of TK.
j
Note j = k1 k /k+1 and 0 = 1. We also have that n = R for n = 0, . . . ,
Introduction to Stochastic Processes
Stat217, Summer 2012
Homework 4 - due in class on Tuesday July 31, 2012
PK = Pinsky and Karlin, Introduction to Stochastic Modeling, 4th edition
(or TK = Taylor and Karlin, Introduction to Stochastic Modeling, 3rd edit
Statistics 202:
Data Mining
c Jonathan
Taylor
Statistics 202: Data Mining
Week 2
Based in part on slides from textbook, slides of Susan Holmes
c Jonathan Taylor
October 3, 2012
1/1
Statistics 202:
Data Mining
c Jonathan
Taylor
Part I
Other datatypes, prep
Box & Cox Transformation
x 1
0
( )
x =
ln x
=0
This is a continuous function of for x > 0
The value of that maximizes the expression,
n
n 1 n ( )
( ) 2
l ( ) = ln x j x
+ ( 1) ln x j
2 n j =1
j =1
n
n x 1
j
( ) 1
( ) 1
where, x = x j =
n j =1
n j =
The points at distance c lie on an ellips with axis given by
the eigenvectors of A and the axes length are proportional
to the reciprocals of the square roots of the eigenvalues.
The constant of proportionality is c.
c
e2
e1
2
c
1
In p - dimensions, the p
Example :
Let X 1 , X 2 , X 3 , X 4 ~ ( , ) where
3
3 - 1 1
= 1, = - 1 1 0
1
1 0 2
Consider alinear combination a X 1 of the three
components of X 1 . It has mean
a = 3a1 a 2 + a3 , a scalar, and variance,
2
2
a a = 3a12 + a 2 + 2a3 2a1 a 2 + 2
Bartlett ' s correction factor to improve the
approximation replaces n with [n-1- (2 p + 4m + 5) 6]
Finally we reject H 0 if
LL +
[n-1- (2 p + 4m + 5) 6]ln
> [2( p m )2 p m ] 2 ( )
S
n
for large p and n-p.
1
2
( p m) p m 2 > 0 m < 2 p + 1 8 p + 1
2
I
Stats-206
Applied Multivariate Analysis
Professor Sadri Khalessi
Summer 2013
Stanford University
Chapter 8
Principle components
Introduction
A PC analysis is concerned about explaining
the variaiance-covariance matrix of a set of
variables x1, x2 ,., x p
Stat 217: Practice Final Exam
March, 2017
The exam consists of six problems. As a resource you may use two pages (four sides) of
notes you have prepared in advance.
1. A chicken lays a Poisson number X of eggs. Each egg hatches with probability p,
indepen
Stat 217: Assignment No. 1
Due Friday, January 20
Read: Chapter 1, except Examples 1.3(B), 1.4(B), 1.5(F), 1.5(G), 1.9(B), and Section
1.5.1.
Work the following Exercises on pages 46-55:
1.1, 1.6, 1.8, 1.11, 1.19, 1.20, 1.23 (Proving the correctness of th
Stat 217: Practice Midterm Exam
The exam consists of three problems. As reference material you are permitted one page
(two sides) of notes that you have prepared in advance.
1. Let Nt be a Poisson process with parmeter , and let Wn denote the waiting time
Stat 217: Assignment No. 4
Due Wednesday, March 1
Read: Chapter 4, Sections 1-5 and Section 7.
Work the following Exercises on pages 219-230.
4.10, 4.15, 4.16, 4.18, 4.21, 4.23, 4.27, 4.30, 4.33 (b), 4.38 (Note that qj should be qij .),
4.39.
(A) Find the
Stat 217: Assignment No. 3
Due Wednesday, February 8
Read: Chapter 3, Sections 1-3 and Section 6.
Work the following Exercises on pages 153-161.
3.3, 3.7, 3.9, 3.11, 3.14 (see the first paragraph on page 116 for the definitions), 3.28.
(A) Let Y1 , Y2 , b