Office Use Only
Monash University
Semester One Examination Period
2006
Faculty Of Science
EXAM CODES:
MTH3251/ETC3510/ETC4351/ETC5351
TITLE OF PAPER:
Financial Mathematics/
Modelling in Finance and Insurance
EXAM DURATION:
3 hours writing time
READING TIM
MTH2232 Mathematical Statistics
Sem 2, 2012
Mid-Semester Test
Name:
Student ID:
Throughout this paper you may use the following facts without proof; simply quote
the reference (F1, F2 etc).
The probability that a normal random variable is within one, two
MTH2232 Mathematical Statistics
1
Tutorial 07 Solution Set
Problems to be submitted at the start of your tutorial
1. =
10(1p)
p
p=
10
;
10+
x
L(p) = Kp10n (1 p)x p =
10
.
10+
x
Problems discussed in tutorials
1. (a) = 0.254, se( ) = 0.018;
(b) = 0.262, se
MTH2232 Mathematical Statistics
1
Tutorial 07 Problem Set
Week 8: Tue 11 Sep & Wed 12 Sep 2012
Problems to be submitted at the start of your tutorial
1. The number of failures before the rth success in a sequence of independent Bernoulli trials
d
with pro
MTH3230 Time Series and Random Processes in Linear Systems,
Semester 2, 2011
Assignment 1. Due in Monday, October 3.
In what follows cfw_Zt is a White Noise with zero mean and variance 2 .
(1) State with the reason (by nding an appropriate time series or
Office Use Only
Monash University
Semester One 2009 Examination Period
Faculty Of Science
EXAM CODES:
MTH3251 / ETC3510
TITLE OF PAPER:
Financial Mathematics / Modelling in Insurance and Finance
EXAM DURATION:
3 hours writing time
READING TIME:
10 minutes
SOLUTIONS MTH3251, ETC3510. 2010
1. Assume the one-step Binomial pricing model for the stock.
(a) Describe all the parameters in the model and give the tree of the stock
prices.
Parameters: d < u for the movement of stock and riskless rate r. S1 = dS0
or
MTH3230 Time Series and Random Processes in Linear Systems
Exercises 4.(covers Section 3.1 of Lecture Notes and 2.1-2.4 of the textbook. Stationary
Processes. Linear Processes. Introduction to ARMA processes. Properties of Sample mean and
Autocorrelation
MTH2232 Mathematical Statistics
1
MTH2232 Sem 2, 2012
Assignment 2
Due Date: 5.00 pm on Friday 21 September 2012
Assignments are to be put in the MTH2232 box on the ground oor of Building 28.
1. Suppose that X has the extreme value distribution with cdf
F
MTH2232 Sem 2, 2012
Assignment 2 - Hints
2.(a) A lognormal random variable is one such that its natural logarithm is normal; that is if
Y is N (, 1), then Z = ln Y is N (, 1). In other words Y can be thought of as eZ where
Z is N (, 1). The answer follows
MTH2232 Mathematical Statistics
1
MTH2232 Sem 2, 2012
Assignment 1
Due Date: 5.00 pm on Wednesday 29 August 2012
Assignments are to be put in the MTH2232 box on the ground oor of Building 28.
1. If a random variable has density f (x) = c x1 , x > c, where
MTH2232 Mathematical Statistics
1
Tutorial 02 Problem Set
Week 3: Tue 7 Aug & Wed 8 Aug 2012
Problems to be submitted at the start of your tutorial
1. Let X1 and X2 be independent exponential random variables with parameter . Find the
pdfs of X(1) and X(2
Chapter 1
RANDOM SAMPLING
1.1 Introduction
A random sample on a random variable X , is a sequence of independent random
variables X1 , X2 , . . . , Xn each having the same distribution as X ; i.e., a random
sample is a set of iidrvs (independent identical
MTH2232 Mathematical Statistics
1
Tutorial 01 Problem Set
Week 2: Tue 31 Jul & Wed 1 Aug 2012
Problems discussed in tutorials
You should attempt these before attending your tutorial.
1. (a) State whether the following are true or false. Give a reason.
n
i
ARMA Modeling and Forecasting (Chap 5)
5.1 Preliminary Estimation
ARMA(p,q) Model: observations x1,., xn,
assume the model
(B) Xt = (B) Zt ,
cfw_Zt ~ WN(0,2),
want to estimate =(1, . . ., p) and =(1, . . ., p) ,
where the orders p and q are assumed known
MTH3230 Time Series and Random Processes in Linear Systems,
Semester 2, 2012
Assignment 1. Due in Friday, September 7.
Assignment 1 is 100 marks which correspond to 15 marks in overall score.
In what follows cfw_Zt is a White Noise with zero mean and var
MTH3230 Time Series and Random Processes in Linear Systems
Exercises 1.
(Covers Basic of Probability: Sections 2.32.6 of LN and Appendix A of the
textbook).
You should attempt these before attending your tutorial. You have to
hand out the solution of the
MTH3230 Time Series and Random Processes in Linear Systems
Exercises 1.(Covers Basic of Probability).
(1) Let (X, Y ) be the independent random variables such that
E(X) = 1,
E(Y ) = 2,
var(X) = 1, var(Y ) = 1.
Find:
(a) E(2X + 3Y ), 1 mark
(b) var(2X + 3Y
MTH2232 Mathematical Statistics
1
Tutorial 05 Solution Set
Problems to be submitted at the start of your tutorial
1. (a) 1.144 < < 1.536;
(b) 1.082 < < 1.598;
(c) c = 1.5045;
(d) > 1.1755.
Problems discussed in tutorials
1. n 62.
2. (a)
i. 1.53 < < 2.28;
MTH2232 Mathematical Statistics
Tutorial 06 Solution Set
Problems to be submitted at the start of your tutorial
1. (a) 1.149 < < 1.531;
(b) 1.088 < < 1.592;
(c) c = 1.660391;
(d) c = 2.364606.
Problems discussed in tutorials
See Tutorial 05.
1
Formula Sheet
Common Random Variables
The Bernoulli Random Variable with probability p of success:
pX (x) = px (1 p)1x , x = 0, 1
E[X ] = p, var(X ) = p(1 p) and MX (t) = (1 p) + pet .
The Binomial Random Variable with n trials and probability p of succ
MTH2232 Mathematical Statistics
Sem 2, 2012
Practice Questions with Hints
The following is a selection of typical questions. They should help you prepare for
the mid-semester test.
Question 1
Let X denote the mean of a random sample of size 100 from a dis
MTH2232 Mathematical Statistics
1
MTH2232 Sem 2, 2012
Assignment 3
Due Date: 5.00 pm on Friday 12 October 2012
Assignments are to be put in the MTH2232 box on the ground oor of Building 28.
1. We shall say that a random variable has distribution D(), wher
MTH3230 Time Series and Random Processes in Linear Systems, semester
2, 2011
Assignment 2. Due in Fri October 21.
In what follows cfw_Zt is a White Noise with zero mean and variance 2 .
(1) Use ITSM to compute and plot the spectral density of the station
MTH3230 Time Series and Random Processes in Linear Systems,
Semester 2, 2011
Assignment 1. Due in Monday, October 3.
In what follows cfw_Zt is a White Noise with zero mean and variance 2 .
(1) State with the reason (by nding an appropriate time series or