Likelihood Ratio Test
Week 9
Goals:
Hypothesis testing with the likelihood function
Review of Hypothesis Testing
State a null hypothesis H0
A statement about the probability model or a parameter in the
model
Be specic, so it is possible to collect evidenc
Stat 231 Tutorial
Week 2 Solutions
1. Consider the following summary statistics taken from a random sample of n = 16
observations,
n
n
2
yi = 1163.56
yi = 106.27,
i=1
i=1
(a) Find the sample mean and sample standard deviation for this data
(b) If we colle
Stat 231 Tutorial
Week 6 Solutions
1. Consider the cell phone example from Week 2 and 4 tutorials. We have previously
seen that a Geometric model appears to t the data. The number of drops for the ith
cell phone to break is recorded as yi (i=1.50) and the
STAT 231-LECTURE 1
Introduc6on
Examples of Sta6s6cal Applica6ons:
From the trivial to the profound
Where have all the 400 hiHers gone?
Gould, Full House,
Ted Williams-Joe DiMaggio
Are experts actually exper
Question I:
The probability that the gestation period of a woman will exceed 9 months is 0314.
a) Let X be the number of human births in which the gestation period exceeds 9 months
among, 6 births. Specify the distribution of X and give the conditions th
Chapter 3
Validation
In many textbooks author will say something like The waiting times between
buses arriving at a bus stop follows from an exponential distribution But.How
.
do we know this is true? It all good and well to say that a set of data follows
Stat 340/CS437 Winter 2001. Final Exam
April 4, 2:00-4:00 P.M.
Instructor: D. L. McLeish
Name.
I.D. .
You are permitted to use a calculator and the formula sheet provided, but no
other aids. All answers should be given in the appropriate place on the exam
Simulation of Complex Systems
Statistics 340, Winter 2013
Section 1 Instructor: Riley Metzger, M3-4202, rametzge@uwaterloo.ca
Section 2 Instructor: Mehdi Molkarie, M3-4018, mmolkaraie@uwaterloo.ca
Office Hours:
Office Hours for instructors and TAs are pos
Chapter 1
Probability
Three approaches to dening probability are:
1. The classical denition: Let the sample space (denoted by S ) be the
set of all possible distinct outcomes to an experiment. The probability of
some event is
number of ways the event can
STAT340 - Winter 2013 Tutorial/Assignment 3
Due Date: Feb 6, 2013
Process: During your weekly tutorial, the TA will give you some questions to work on. S/he will take
them up with you during the tutorial period. You will be given a grade for handing in th
STAT340 - Winter 2013 Tutorial/Assignment 2
Due Date: Jan 30, 2013
Process: During your weekly tutorial, the TA will give you some questions to work on. S/he will take
them up with you during the tutorial period. You will be given a grade for handing in t
STAT340 - Winter 2013 Tutorial/Assignment 2
Due Date: Jan 30, 2013
Process: During your weekly tutorial, the TA will give you some questions to work on. S/he will take
them up with you during the tutorial period. You will be given a grade for handing in t
STAT340 - Winter 2013 - Tutorial/Assignment 1
Due Date: Jan 23, 2013
Process: During your weekly tutorial, the TA will give you some questions to work on. S/he will take them up
with you during the tutorial period. You will be given a grade for handing in
STAT340 - Winter 2013 - Tutorial/Assignment 1
Due Date: Jan 23, 2013
Process: During your weekly tutorial, the TA will give you some questions to work on. S/he will take them up
with you during the tutorial period. You will be given a grade for handing in
Oct 8th
Expectation
Formula:
Concept:
Populations Vs Samples
Pictorially:
Populations vs Samples
Example:
e.g. a)
I roll la die 3 times and get 3, 2, 4 What is the sample mean?
b)
What is the expected value?
Variance
Formula:
Concept:
e.g. a)
I roll la di
Hypothesis Tests (HT) Methodology
Particular Recipe for HT Sigma UNknown
1. Determine the hypotheses 2. Use the formula:
3. Calculate a p value:
4. Make a conclusion
A "Nermal" Curve
Example
8 Northern Ontario Lakes pH levels are measured. The average is
BHP Struggles to Dig Into Its Cash
Mountain
BHP Billiton is finding success a headache
UBS estimates its share price trades at a 12%
discount to the company's net present value
Many investors are clamoring for BHP to return
the cash via increased share
Ch25 Options
Value of Options at Expiration
Combinations of Options
Valuing Options: Various approaches
Stocks and Bonds as Options
Recommended problems
Ch24: Questions and problem 3-7
Ch25: Questions and problem 2, 3, 4, 6, 7
A.1, A.2 on Page 784, A.3 on
Ch24 Risk Management
An Introduction to Financial
Engineering
Hedging and Price Volatility
Managing Financial Risk
Hedging with Forward, Futures, Swap and
Option Contracts
24-1
LO1
Hedging Volatility 24.1
Return Volatility is a classic measure of risk
Chapter 23 Mergers and Acquisitions
The Legal Forms of Acquisitions
Taxes and Acquisitions
Accounting for Acquisitions
Pros and Cons of M&A
Defensive Tactics
Evidence on Acquisitions
Divestitures and Restructurings
23-1
Canada becomes the destination of c