THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
June 2011 Examination
MATH2901
HIGHER THEORY OF STATISTICS
(1) TIME ALLOWED 2 hours
(2) TOTAL NUMBER OF QUESTIONS 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE OF EQUAL VALUE
(5) TH
MATH2801 Theory of Statistics
Semester 1, 2017
Assignment 1 Probability and Random variables
Important skills to demonstrate:
Ability to use key theoretical tools to derive and explore the properties of probability
and of random variables, and to present
Chapter 0
Probability
Statistics is all about making decisions based on data in the presence of uncertainty. In
order to deal with uncertainty we need to develop a language for discussing it probability
theory. We will also derive in this chapter some fun
MATH2901 JUNE 2012 SOLUTIONS
Question 1
a) Each of the n2 animals has n1 /T probability of being one of the previously captured animals,
so X2 Bin(n2 , n1 /T ). The expected value of X2 is n1 n2 /T , so we might expect that
n1 n2
n1 n2
= T.
T =
X2
n1 n2 /
Dirk P. Kroese and Joshua C.C. Chan
Statistical Modeling and
Computation
An Inclusive Approach to Statistics
February 18, 2013
Springer
Chapter 4
Common Statistical Models
The conceptual framework for statistical modeling and analysis is sketched in
Figur
FACULTY OF SCIENCE
SCHOOL OF MATHEMATICS AND
STATISTICS
MATH2801/2901
(HIGHER) THEORY OF
STATISTICS
Semester 1, 2013
Contents
MATH2801/MATH2901 Course Outline
Probability Revision
i
ix
Lecture Notes Part One Probability and Distribution Theory
1
1 Random
Probability Revision
Statistics is all about making decisions based on data in the presence of uncertainty. In order to deal with uncertainty we need to develop a language for discussing it probability theory. We will also derive in this chapter some fund
Dirk P. Kroese and Joshua C.C. Chan
Statistical Modeling and
Computation
An Inclusive Approach to Statistics
February 18, 2013
Springer
In memory of Reuven Rubinstein, my
Friend and Mentor
Dirk Kroese
To Raquel
Joshua Chan
Preface
Statistics provides one
MATH2901 (Higher) Theory of Statistics
Semester 1, 2013
Chapter 0 solutions
1.
i) A B C
ii) A B C
iii) (A B) (A C) (B C)
iv) (A B C) (A B C) (A B C)
v) (A B C) (A B C) (A B C)
2. Most professional basketball players are tall, but it is not true that most
MATH2801 Assignment 1
1. (a) Graphical summary
Numerical summary:
I typed the command
cor(happyhour$BAC,happyhour$StandardDrinks)
in RSStudio, then the output is [1] NA and the reason is that there are NAs in the variables.
So I put another command instea
Solution to MATH2901 Assignment 1
Question 1
(i) If P(A) = 0, then by result 4. on page 11 and Axiom 1. on page 10 of the course pack
0 P(A B) P(A) = 0
this implies P(A B) = P(A)P(B) = 0.
If P(A) = 1, then
P(A B) = P(A) + P(B) P(A B)
= 1 + P(B) 1
= P(A)P(
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SIGNATURE: .
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
May 2015 Examination
MATH2901
HIGHER THEORY OF STATISTICS
1 TIME ALLOWED 45 minutes
(
(2 TOTAL NUMBER OF QUESTIONS 2
(3 A
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
June 2012 Examination
MATH2901
HIGHER THEORY OF STATISTICS
(1) TIME ALLOWED _ 2 hours
(2) TOTAL NUMBER OF QUESTIONS A 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE OF EQUAL VALUE
(5
Assignment 3. Solution
1. One way classification model
(a) The summary output of the fitted model
Call:
lm(formula = Time ~ Format, data = Timeformat)
Residuals:
Min
1Q Median
-2.060 -1.000 -0.100
3Q
0.725
Max
1.800
Coefficients:
Estimate Std. Error t val
COURSE OUTLINE
MATH2831
Linear Models
Semester 2, 2015
Cricos Provider Code: 00098G Copyright 2015 -School of Mathematics and Statistics, UNSW
MATH2831/2931 Course Outline
Information about the course
Course Authority: Dr. Libo Li
Lecturers: Dr. Libo Li,
MATH2931 Assignment 2 - solutions
Question 1
(i) To show that Icfw_xc < et(cx) . For t > 0. If x c, then et(cx) > 1 = Icfw_xc . If x > c, then
et(cx) > 0 = Icfw_xc .
This implies Icfw_Xi c < et(cXi ) and for 0 < t < h, by taking expectation of both sides,
1
P-values
Often it is more informative to report a value which indicates the strength of the evidence against
against H0 rather then the dry cut reject or not reject. This helps the decision maker in making a
more informed decision. The P-value is one wa
Assignment 2. Solution
1. (a) The F -statistic is given in the summary output
F-statistic: 192.3 on 4 and 35 DF,
p-value: < 2.2e-16
The conclusion of the F-test under a 1% level is that we reject H0 .
(b) In the full model, to test the hypothesis that
AP
MATH2901 (Higher) Theory of Statistics
Semester 1, 2013
Chapter 0 solutions
1.
i) A B C
ii) A B C
iii) (A B) (A C) (B C)
iv) (A B C) (A B C) (A B C)
v) (A B C) (A B C) (A B C)
2. Most professional basketball players are tall, but it is not true that most
MATH2901 (Higher) Theory of Statistics
Semester 1, 2013
Chapter 0 solutions
1.
i) A B C
ii) A B C
iii) (A B) (A C) (B C)
iv) (A B C) (A B C) (A B C)
v) (A B C) (A B C) (A B C)
2. Most professional basketball players are tall, but it is not true that most
3.4 Bayes' Rule
In general, if A and B are given events, then from the multiplication rule we have:
P (A B) = P (A)P (B|A) = P (B)P (A|B)
then by dividing both sides with
P (B),
we obtain Bayes' Rule:
P (A|B) =
P (A)P (B|A)
P (B)
but note that:
P (B) = P
Meal
Mean
SD
Breakfast
500
50
Lunch
800
100
Dinner
1700
200
4.5.2 Central Limit Theorem
If the samples are not from a normal population, then for sample sizes of
n 30,
the Central
Limit Theorem suggests that the approximate distribution of the sample aver
3.2 Probability Concepts
1. The probability of any event must lie between 0 and 1. That is
0 P (A) 1
for any
event A.
2. The total probability assigned to the sample space of an exerperiment must be 1. For
a sample space S, then
P (S) = 1.
3. The probabil
3 Probability
Probability models contain two components:
A description of the possible outcomes that can be observed
The probability of each outcome or sets of outcomes
3.1 Chance Experiments
A chance or random experiment is simply an activity or situatio
6 Statistical Quality Control
Statistical Quality Control is concerned with monitoring process and product to determine if
expected levels of variation in quality are occuring or if something is happening that produces
unusuay process or product outcomes.
2.4.6 The 5 number summary
The 5 number summary describes the distribution of the data in a set:
smallest data value,
Q1 ,
There are dierent ways of calculating
median,
Q3 ,
Q1 and Q3 .
largest data value
One way is to divide the ordered data
sets into 2
4 Random Variables, Population &
Sampling Distributions
4.1 Random Variables
A random variable is a function that assigns a real number to each outcome in the sample
space of a random experiment. A random variable is denoted by an uppercase letter such as
5.3 Sampling Distribution of proportions
Recall that if there are n observations each with 2 possible outcomes, the distribution of
the count X of the number of successes is a binomial distribution with parameters n and
.
However, when n is large, the sam