THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913
Assignment 1 - Due on Tuesday of Week 6 by 4.00pm
2
1. Let X1 , X2 , , Xn be iid random variables with mean and variance 2 and Var(X1 ) < +. Show
2
that n1
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913 - Week 4
Tutorial Exercise
1. Let X n be the sample mean of size n from a distribution that has the pdf, f (x) = ex , x (0, +)
and the characteristic functi
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913 - Week 3
Tutorial Exercise
1. When X1 and X2 are iid uniform rvs on (0, 1), it is known that the pdf of Y = XX12 , fY (y) is 1/2 for
0 < y 1 and 2y12 for y
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913 - Week 2
Tutorial Exercise
1. A professor of statistics has two boxes of computer disks: box C1 contains 7 V disks and 3 C disks
and box C2 contains 2 V dis
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913 - Week1
Tutorial Exercise
1. There are 32 children in a class room. What is the probability that at least two of them will have
the same birthday? Assume 36
The University of Sydney
Statistical Inference: STAT3013/3913
Semester 2
Computer Class Week 11
2013
In this prac we will repeat Week 9 Lab with a beta distribution. The beta distribution has
density function
( + ) 1
f (x; , ) =
x (1 x) 1 ,
()( )
where 0
The University of Sydney
Statistical Inference: STAT3013/3913
Semester 2
Computer Class Week 11
2013
In this prac we will repeat Week 9 Lab with a beta distribution. The beta distribution has
density function
( + ) 1
f (x; , ) =
x (1 x) 1 ,
()( )
where 0
STAT3013/3913: Lab in week 10
Maximum likelihood estimation: Application
Semester 2, 2013
The gamma distribution has been used widely in diverse applications
from insurance losses to wind farm output. It has positive support
and is therefore suitable for
STAT3013/3913: Lab in week 10
Maximum likelihood estimation: Application
Semester 2, 2013
The gamma distribution has been used widely in diverse applications
from insurance losses to wind farm output. It has positive support
and is therefore suitable for
STAT3013/3913: Lab in week 9
MLE for gamma distributions
Semester 2, 2013
Suppose we wish to t a gamma distribution with density
x 1 e x /
,
()
f ( x ; , ) =
for x > 0 to some data x1 , x2 , . . . , xn by maximum likelihood.
The log-likelihood is
n
L(,
STAT3013/3913: Lab in week 9
MLE for gamma distributions
Semester 2, 2013
Suppose we wish to t a gamma distribution with density
x 1 e x /
,
()
f ( x ; , ) =
for x > 0 to some data x1 , x2 , . . . , xn by maximum likelihood.
The log-likelihood is
n
L(,
STAT3013/3913: Lab in week 8
Maximum likelihood estimation
Semester 2, 2013
1. Let X1 , . . . , Xn be independent uniform variates on the interval
( 1 , 2 ).
(a) Using a similar method to the week 7 lab, generate 1000 samples of size n = 20 standard unifo
STAT3013/3913: Lab in week 8
Maximum likelihood estimation
Semester 2, 2013
1. Let X1 , . . . , Xn be independent uniform variates on the interval
( 1 , 2 ).
(a) Using a similar method to the week 7 lab, generate 1000 samples of size n = 20 standard unifo
STAT3013/3913: Lab in week 7
Efciency calculations using simulation
Semester 2, 2013
In this prac we will perform a basic simulation study comparing the
performance of the mean and median as estimators of location.
1. Generate a pseudo-random sample of 10
STAT3013/3913: Lab in week 7
Efciency calculations using simulation
Semester 2, 2013
In this prac we will perform a basic simulation study comparing the
performance of the mean and median as estimators of location.
1. Generate a pseudo-random sample of 10
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913
Assignment 2 - Due on Tuesday of Week 12 by 4.00pm
1. Let X1 , , Xn be iid random variables with density
f (x| ) = e x ,
x (0, +),
where (0, +) and n 2.
(a)
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913
Assignment 2 - Due on Tuesday of Week 12 by 4.00pm
1. Let X1 , , Xn be iid random variables with density
f (x| ) = e x ,
x (0, +),
where (0, +) and n 2.
(a)
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913
Assignment 1 - Due on Tuesday of Week 6 by 4.00pm
2
1. Let X1 , X2 , , Xn be iid random variables with mean and variance 2 and Var(X1 ) < +. Show
2
that n1
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Statistical Inference: STAT3013/3913 - Week 5
Note: There will be a quiz in your tutorial class of Week 6. This is a closed book examination.
NO MAKE-UP QUIZZES ARE AVAILABLE.
NON PARTICIPANTS