NATIONAL UNIVERSITY OF SINGAPORE
NUS Business School
Department of Decision Sciences
DSC5103 Statistics
Lecturer
:
Assistant Prof Wang Tong
Session
:
Semester I, 2015/2016
Aims & Objectives
This course aims to provide a holistic overview of the modern Sta
ST5202 Homework 2
Due: Feb. 27th 2017 by 8:30 pm in class
Note: please dont forget to write down your name and ID when
you turn in your homework
1. Suppose we have two linear models with k > p such that
Mp : Y
=
0 + 1 X1 + + p1 Xp1 +
and Mk : Y
=
0 + 1 X
Chapter 4
Random Variables
4.1
Random Variables
In many situations when an experiment is performed, we are interested
in some function of the outcome rather than the outcome itself. Here are
some examples:
Example 4.1. When we roll a pair of dice, lets sa
Chapter 3
Conditional Probability and
Independence
3.1
Introduction
In many problems, we are interested in event B. However, we have some
partial information, namely, that an event A has occurred. How to make
use of this information?
In calculating P(B),
Chapter 2
Axioms of Probability
2.1
Introduction
In this chapter we introduce the basic terminology of probability theory:
experiment, outcomes, sample space, events. Next we define what the
probability of an event is and proceed to show how it is compute
Chapter 1
Combinatorial Analysis
1.1
Introduction
Many problems in probability theory can be solved simply by counting the
number of different ways that a certain event can occur. Effective methods
for counting would then be useful in our study of probabi
NATIONAL UNIVERSITY OF SINGAPORE
ST1131 Introduction to Statistics
Midterm Test
Time Allowed: 60 minutes
SEAT No:_
Tutorial Group:_T_[for collection of the midterm paper from your tutor]
NAME: _
Answer all questions. You are required to write in the space
NATIONAL UNIVERSITY OF SINGAPORE
ST1131 cfw_ INTRODUCTION TO STATISTICS
Semester I : 2013cfw_2014
Names of examiners : Associate Professor Gan Fah Fatt/Ms Wong Yean Ling
November / December 2013
Time allowed : 2 hours
INSTRUCTIONS TO CANDIDATES
1. Please
More examples of stationary distributions and
limiting behaviour
February 7, 2017
Doubly stochastic chains
Definition
A transition matrix p is saidPto be doubly stochastic if its
columns sum to 1, that is, x p(x, y ) = 1.
We have seen in a tutorial proble
Exit distributions
February 10, 2017
Example: American two year college
At an American two year college, 60% of first year students
become second year students, 25% remain in the first year, and
15% drop out. 70% of second year students graduate (and tran
Classification of states: Recurrence and
transience
January 16, 2017
Example of recurrence: Social mobility
Recall the social mobility model, which is a Markov chain with
three states (1 = lower class, 2 = middle class, and 3 = upper
class), and the trans
Multistep transition probabilities
January 13, 2017
Multistep transition probability by example
Recall that the transition probability for a Markov chain
i
p(i, j) = P(Xn+1 = j | Xn = k)
= P(Xn+1 = j | Xn = i, Xn
1
= in
1 , . . . , X0
= i0 ).
It means tha
Review of probability concepts and examples of
Markov chains
January 10, 2017
Probability
A probability theory begins with a probability space that consists
of a set called sample space usually denoted by , and a function
called probability, usually denot
Spatial Point Patterns
1
Introduction
In many contexts, data arises in the form of a set of points, irregularly distributed
within a region of space.
E.g. Locations of certain tree species in a forest.
E.g. Nests in a breeding colony of birds
Note tha
Projections, Import & Export
Vik Gopal
ST5226 Spatial Statistics
Topic 04
1
1
Introduction
2
Coordinate Reference Systems (CRS)
3
Data Import And Export
ESRI Format
KML Format
4
Further Methods
Combining Spatial Features
Spatial Joins
5
Index of Examples
Chapter8
Factor Analysis
ST5210MultivariateDataAnalysis
CYM
8.1
8.1Introduction
Factor analysis (F.A.) methods are widely used in
the Behavioral and Social Sciences.
The basic purpose of F.A. is to describe the
covariance relationships among many vari
R Classes for Spatial Data
Vik Gopal
ST5226 Spatial Statistics
Topic 02
1
1
Classes and Methods in R
Dataframes and Lists
Some Useful Functions
S3 and S4 Classes
2
Spatial Objects in R
Spatial Class
SpatialPoints* Classes
SpatialLines* Classes
SpatialPoly
Regional / Lattice Data
1
Introduction
In many situations, we cannot obtain point-level data due to confidentiality issues.
Instead, we obtain disease, census or other data only as summary counts for a particular
set of districts.
The observed data are
Geostatistics
1
Introduction
Geostatistical data are data that could, in principle, be measured anywhere within
a domain of interest. Examples of such data are:
Gold grades within a gold mine.
Particulate Matter (PM) in air samples.
Unlike in a point
Chapter 10
Cluster Analysis
ST5210 Multivariate Data Analysis
CYM
10.1
10.1 Introduction
Clustering is essentially an exploratory procedure
where given a dataset our aim is to group objects
into a number of groups, the number of which is
also to be de
Chapter 5
Estimation and Hypothesis Testing
ST5210 Multivariate Data Analysis
CYM
5.1
5.1 Estimation
In parametric statistics, is a k-variate vector
characterizing the unknown properties of the
population pdf
The aim will be to estimate from the sample
ST3241 Categorical Data Analysis I
Semester II, 2012-2013
Solution to Tutorial 1
1. (a) Nominal.
(b) Ordinal.
(c) Ordinal.
(d) Nominal.
(e) Nominal.
2. As the student selects one answer randomly out of four possible choices, the prob- ability
that the stu
ST3241 Categorical Data Analysis I
Semester II, 2012-2013
Tutorial 7
1. For a study using logistic regression to examine the data on rheumatoid arthritis, we
consider age of the patient as the predictor variable. The response Y measured whether
the patien
ST3241 Categorical Data Analysis I
Semester II, 2012-2013
Tutorial 4
1. For baseball national league games during nine decades, the following table shows the
percentage of times that the starting pitcher pitched a complete game.
Decade
Percent
Complete
19
ST3241 Categorical Data Analysis I
Semester II, 2012-2013
Tutorial 6
1. The U.S. National Collegiate Athletic Association (NCAA) conducted a study of graduation rates for student athletes who were freshmen during the 19841985 academic year.
The following
ST3241 Categorical Data Analysis I
Semester II, 2012-2013
Tutorial 2
1. The following table was taken from the 1991 General Social Survey.
Belief in Afterlife
Race
Yes
No or Undecided
White
Black
621
89
239
42
(a) Identify each classification as a respons