MA2172
1.
Assignment 3
2014/15 Semester A
Final averages are typically approximately normally distributed with a mean of 72 and a
standard deviation of 12.5. Your professor says that the top 8% of the class will receive an A;
the next 20%, a B; the next 4
MA2172 Applied Statistics for Sciences and Engineering
Examples on Chapter 4  Bayes Rule
Statistics needed: Bayes Rule, Conditional probability, Complement of an event, Rules of
probability, Multiplication rule, Independence
1.
(E0607B_Q1C). The probabil
MA2172 Applied Statistics for Sciences and Engineering
Examples on Chapter 4 More Problems on Probability
Statistics needed: Conditional probability, Addition rule, Multiplication rule, Independence,
Equally likely events, Complement of an event
1.
(T0304
* This is about wave equation on the whole domain from Chapter 2. Given a domain
D = (, ) (0, ), we denote wave equation by
utt = c2 uxx on D,
(W )c .
(1) (TP38Exc1) Solve (W )c with datum
u(x, 0) = ex , ut (x, 0) = sin x, x R.
(2)
Let c2 = T /. Solve (W
MA2172 Applied Statistics for Sciences and Engineering
Examples on Chapter 5  Binomial Distribution
Statistics needed: Binomial probability distribution, Binomial probability function, Mean and
standard deviation of the binomial distribution
1.
(E0607B_Q
MA2172 Applied Statistics for Sciences and Engineering
Examples on Chapter 5  Probability Distribution
Statistics needed: Properties of probability, Probability distribution, Probability function, Mean
and standard deviation of a discrete/continuous rand
* This is about wave equation on the whole domain from Chapter 2. Given a domain
D = (, ) (0, ), we denote wave equation by
utt = c2 uxx on D,
(W )c .
(1) (TP38Exc1) Solve (W )c with datum
u(x, 0) = ex , ut (x, 0) = sin x, x R.
Proof.
1
1
u = (ex+ct + ex
MA3512: Partial Differential Equations
Fall 2015
Lecture 6: Maximum Principle & Fourier Series (I)
Lecturer: Xianpeng Hu
Dates: October 9
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be d
MA3512: Partial Differential Equations
Fall 2015
Lecture 3: Wave Equation (II): Separation of Variables
Lecturer: Xianpeng Hu
Dates: September 18
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They
MA3512: Partial Differential Equations
Fall 2015
Lecture 4: Heat Equation (I)
Lecturer: Xianpeng Hu
Dates: September 25
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outside
MA3512: Partial Differential Equations
Fall 2015
Lecture 1: Introduction to PDEs
Lecturer: Xianpeng Hu
Dates: September 4
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outsi
MA3512: Partial Differential Equations
Fall 2015
Lecture 11: Fourier Transform and Laplace Transform
Lecturer: Xianpeng Hu
Dates: November 20
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may
MA3512: Partial Differential Equations
Fall 2015
Lecture 5: Heat Equation (II)
Lecturer: Xianpeng Hu
Dates: October 2
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outside t
MA3512: Partial Differential Equations
Fall 2015
Lecture 8: Poissons Equation (I)
Lecturer: Xianpeng Hu
Dates: October 23
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outsi
MA3512: Partial Differential Equations
Fall 2015
Lecture 9: Poisson Equations (II)
Lecturer: Xianpeng Hu
Dates: October 30
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outs
MA3512: Partial Differential Equations
Fall 2015
Lecture 2: Wave Equation (I)
Lecturer: Xianpeng Hu
Dates: September 11
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outside
MA3512: Partial Differential Equations
Fall 2015
Lecture 7: Fourier Series (II)
Lecturer: Xianpeng Hu
Dates: October 16
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outside
MA3512: Partial Differential Equations
Fall 2015
Lecture 10: General Eigenvalue Problems
Lecturer: Xianpeng Hu
Dates: November 6
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distribute
jQuery Selectors
A jQuery Selector is a function which makes
use of expressions to find out matching
elements from a DOM based on the given
criteria.
1
The $() factory function
jQuery
Tag Name:
Tag ID:
Tag Class:
Description
Represents a tag name availab
MA1200 Calculus and Basic Linear Algebra I
Semester A 2016/2017
Course Information
1. OBTL and course webpage of MA1200
(a) MA1200 adopts OBTL practice.
(b) Please visit the MA1200 Canvas regularly for any update (announcements, course materials,
etc.)
2.
Mathematical Models and Methods in Asset Management
MATHEMATIC MA 5623

Fall 2013
Exam Advice
You will find helpful advice about common errors in the Examiners Reports. Some specific
examples are dealt with here.
All modules
The OCR Report on the Units taken in June 2006 contains a statement of the rules
examiners use when they see rep
TFA 33 (19711973) 187189
187
REVIEW
THE ANALYSIS
OF MORTALITY
AND
OTHER ACTUARIAL
STATISTICS
by
B. Benjamin, Ph.D., F.I.A. and the late H. W. Haycocks
Pp. viii+ 392. Cambridge University Press. 3.00
Dr. Benjamin pays tribute in the Preface to his coaut
Chapter 11 ValueatRisk
Junhui Wang
Department of Mathematics
City University of Hong Kong
Semester A, 2015
Wang, Junhui
VaR
VaR
widely used to measure risk of all types of securities
relies on two parameters
T : horizon
1 : confidence level
VaR is a bou
Chapter 12 GARCH Models
Junhui Wang
Department of Mathematics
City University of Hong Kong
Semester A, 2015
Wang, Junhui
GARCH
ARMA model: recap
ARMA models Yt as a linear function of the past plus a white
noise term
(1 1 B p B p )(Yt ) = (1 1 B q B)t
a r
Chapter 2 Probability and Statistical Models
Junhui Wang
Department of Mathematics
City University of Hong Kong
Semester A, 2015
Wang, Junhui
Some Basics
Some basic concepts and facts
Random experiment generates one of many possible outcomes.
Sample space
Chapter 3 Returns
Junhui Wang
Department of Mathematics
City University of Hong Kong
Semester A, 2015
Wang, Junhui
Returns
Price and returns
Let Pt be the price of an asset at time t.
Assuming no dividends the net return is
Rt =
Pt
Pt Pt1
1=
.
Pt1
Pt1
The
Chapter 5 Portfolio Theory
Junhui Wang
Department of Mathematics
City University of Hong Kong
Semester A, 2015
Wang, Junhui
Portfolio
Portfolio selection
How should we invest our wealth? Two principles:
maximize expected return
minimize risk
Tradeoff betw
Chapter 10 Resampling
Junhui Wang
Department of Mathematics
City University of Hong Kong
Semester A, 2015
Wang, Junhui
Bootstrap
Bootstrap
To pull oneself up by ones
bootstraps; attributed to a
German folktale where the
main character tries to pull
himsel
Chapter 6 Regression
Junhui Wang
Department of Mathematics
City University of Hong Kong
Semester A, 2015
Wang, Junhui
Regression
Regression
regression is one of the most popularly used statistical
methods
available data: (Xi , Yi )ni=1
Yi : response varia
Chapter 9 Fixed Income Securities
Junhui Wang
Department of Mathematics
City University of Hong Kong
Semester A, 2015
Wang, Junhui
Bonds
Securities
owning a share of stock means partial ownership
share in both the profits and losses
nothing is guaranteed