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 1 (the middle value).
But what exactly do we mean by ex
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 discount
Force of interest
Understand mathematical and
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
d ( m)
Perpetuities
General proof for
a
1
i
1. Let X a
THE AUSTRALIAN NATIONAL UNIVERSITY
RESEARCH SCHOOL OF FINANCE, ACTUARIAL STUDIES AND APPLIED
STATISTICS
FINANCIAL MATHEMATICS (STAT 2032 / STAT 6046)
SEMESTER TWO 2015
ASSIGNMENT
Due Date: Friday 23 October 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
activated. Current ows if the event C happens, where
C = (R1 R
RESEARCH SCHOOL OF FINANCE, ACTUARIAL
STUDIES AND APPLIED STATISTICS
INTRODUCTORY MATHEMATICAL STATISTICS /
PRINCIPLES OF MATHEMATICAL STATISTICS
(STAT2001/6039)
Assignment 2 Semester 2 (2015)
Your solutions to the assignment should be placed in the appr
STAT6039
Principles of Mathematical Statistics
Course Description
A first course in mathematical statistics with emphasis on applications; probability, random
variables, moment generating functions and correlation, sampling distributions, estimation of
pa
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
Point
and
Estimation
Statistics The Australian National
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 Studies
Sampling
andDistributions
Statistics The Australi
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 Studies
Centraland
Limit
Statistics
Theorem
The Australian
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. Let's now discuss some others.
Efficiency
Suppose tha
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 distributions as follows:
If the mgf of a rv X is the same
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(2,1/2).
1/ 4, y = 0
So p ( y ) = 1/ 2, y = 1
1/ 4, y =
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 rolled. Let X = no. of 6s and Y = no. of even numbers.
Fi
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 ) P ( A j ) i < j ).
For example A1 , A2 , A3 are pair
STAT2001_CH01 Page 1 of 7
INTRODUCTORY MATHEMATICAL STATISTICS
(STAT2001/6039)
LECTURE NOTES
OVERVIEW (or PREVIEW)
Introduction (Chapter 1 in textbook)
What is statistics? Basic concepts. Summarising (or characterising) a set of numbers,
graphically and n
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 number; it cannot be a letter, say.
More precisely, 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 1
Ys pdf is
Let Y be the number of heads that come up o