STAT2001_CH03B Page 1 of 7
Expectation
Two coins are tossed. How many heads can we expect to come up?
1/ 4, y = 0
Let Y = number of heads. Then p( y ) = 1/ 2, y = 1
1/ 4, y = 2
The answer seems to be
STAT 2032/6046
FINANCIAL MATHEMATICS
Abhinav Mehta
Week 3
Recap
Simple and compound interest
Present value and accumulated value
Effective and nominal rates of interest
Effective and nominal rates of
STAT 2032/6046
Financial Mathematics
Abhinav Mehta
Week 4
Perpetuities
Payments continue forever
Examples:
income from real estate, company dividends
1
a|
i
(m
a|)
Proof?
1
i ( m)
a|
1
d
(m
a|)
1
THE AUSTRALIAN NATIONAL UNIVERSITY
RESEARCH SCHOOL OF FINANCE, ACTUARIAL STUDIES AND APPLIED
STATISTICS
FINANCIAL MATHEMATICS (STAT 2032 / STAT 6046)
SEMESTER TWO 2015
Problem 2
(a)
Let R1 be the event that relay 1 closes properly when activated, R2 be the event that relay
2 closes properly when activated and R3 be the event that relay 3 closes properly when
activat
RESEARCH SCHOOL OF FINANCE, ACTUARIAL
STUDIES AND APPLIED STATISTICS
INTRODUCTORY MATHEMATICAL STATISTICS /
PRINCIPLES OF MATHEMATICAL STATISTICS
(STAT2001/6039)
Assignment 2 Semester 2 (2015)
Your s
STAT6039
Principles of Mathematical Statistics
Course Description
A first course in mathematical statistics with emphasis on applications; probability, random
variables, moment generating functions an
Point Estimation
Yanrong Yang
Research School of Finance, Actuarial Studies and Statistics
The Australian National University
April 24, 2017
Yanrong Yang Research School of Finance, Actuarial Studies
Sampling Distributions
Yanrong Yang
Research School of Finance, Actuarial Studies and Statistics
The Australian National University
April 19, 2017
Yanrong Yang Research School of Finance, Actuarial St
Central Limit Theorem
Yanrong Yang
Research School of Finance, Actuarial Studies and Statistics
The Australian National University
April 20, 2017
Yanrong Yang Research School of Finance, Actuarial Stu
STAT2001_CH09A Page 1 of 8
PROPERTIES OF ESTIMATION
AND METHODS OF ESTIMATION (Chapter 9)
Weve already looked at several properties of point estimators in Chapter 8,
for example bias, variance and MSE
STAT2001_CH06B Page 1 of 4
The moment generating function method (Thm 6.1)
Recall that the moment generating function (mgf) of a random variable X is
mX (t ) = Ee Xt .
Mgfs can be used to identify dis
STAT2001_CH06A Page 1 of 6
FUNCTIONS OF RANDOM VARIABLES (Chapter 6)
The discrete case
Example 1
A coin is tossed twice. Let Y be the number heads that come up.
Find the dsn of X = 3Y 1.
Here, Y ~ Bin
STAT2001_CH05A Page 1 of 9
MULTIVARIATE PROBABILITY DISTRIBUTIONS
(Chapter 5)
Well first look at the discrete case; the continuous case will be discussed later.
The discrete case
Example 1
A die is ro
STAT2001_CH02C Page 1 of 12
Generalisations to several events
Pairwise independence
Events A1 , , An are said to be pairwise independent
if each pair of them are independent (ie, P ( Ai A j ) = P ( Ai
STAT2001_CH03A Page 1 of 10
DISCRETE RANDOM VARIABLES (Chapter 3)
A random variable (rv) is a numerical variable whose value depends on the outcome
of an experiment.
Notes: A random variable must be a
STAT2001_CH04A Page 1 of 7
CONTINUOUS RANDOM VARIABLES (Chapter 4)
Cumulative distribution functions
The (cumulative) distribution function (cdf) of a random variable Y is
F ( y ) = P(Y y ) .
Example