Conditional probability
Conditional probability
So far, all (unconditional) probabilities were calculated with respect
to the sample space S.
However, in many situations, we can obtain some new information
such that we can update the sample space.
More sp
MGMT 4210
Corporate Strategy
Prof. Pavel Zhelyazkov
2/11/2016
MGMT 4210 - Corporate Strategy - Prof. Pavel Zhelyazkov
1
International strategy
2/11/2016
MGMT 4210 - Corporate Strategy - Prof. Pavel Zhelyazkov
2
Today we focus on how firms manage
external
MGMT 3140 - Fall 2016
EXAMINATION I: Sample (Answers)
Name _
Student Number_
Section Number_
*Please put your name and student number on the question paper and the multiple
choice answer sheet *
*Please return the question paper and the multiple choice an
Column
Right (R)
Group 3
Group 2
Column
Center (C)
Group 6
Column
Left (L)
Group 7
Group 5
Group 10
Group 9
Group 1
Group 4
Group 8
Group 1
Group 4
Group 8
LSK1005 Seating Plan
Teacher's Desk
SCREEN
DOOR
Counting sample points
What is the number of different ways to order distinct objects?
For example, suppose that there are 5 people, say
A B C D E
Now,
Now we want to arrange them in a row randomly
randomly,
then how many ways are possible?
Consider the f
Review
Probability
obab ty
be a measure of the possibility that a random phenomenon occurs,
t find th regularity of these random phenomena.
to fi d the
l it f th
d
h
Basics of probability theory
p
y
y
Sample space
Complement
Element (or sample point)
Permutation
Permutation
Theorem
The number of permutations of n distinct objects is n!.
In general, the number of permutations of n distinct objects
taken r n at a time is
n!
n(n 1)(n 2) (n r 1)
(n r )!
There are r terms
denoted by
n
r
P
(Linear) Permuta
Random Variables and
Probability Distributions
On page 3 of lecture note 2
Question 1: Flip a fair coin three times. List all the possible
outcomes, i.e. find the sample space of this experiment.
S = cfw_ HHH, HHT HTH, THH TTH THT, HTT , TTT .
,
,
,
Varia
Independence
Irrelevant information
Based on a new information, we can update the sample space and
events to be new ones, so that we can calculate a conditional probability
of the updated event.
However, sometimes, the new information may be irrelevant.
T
Circular permutation
There are n! different permutations of n di ti t
Th
! diff
t
t ti
f distinct
(
objects. arranged in a line ).
How about other kinds of arrangement?
Say, if the people are randomly arranged in a
circle, how many different ways do we ha
Probability
y
Originate from the study of games of chance and gambling during the
16th century.
Be a measure of the possibility that a random phenomenon occurs,
e.g. the tossing of a dice.
Although we cannot exactly predict what we get in any random
p
p
Math
M th 2411 A li d St ti ti
Applied Statistics
(Spring, 2012)
by
Dr. Yu, Chi Wai
Instructor: Dr. Yu, Chi Wai
Office: Room 3492
Email: [email protected]
Course webpage: http:/www.math.ust.hk/~macwyu/
Office Hours:
14:00-14:50 (Mon,
14:00 14:50 (Mon Tue) or
Math2411 (2013, Fall)
Introduction to R
Part II: Statistics
1
Introduction to R
Risafreestatisticalprogramminglanguage.
Downloadat:http:/www.rproject.org.
Or, simply google [R], it should appear as the first hit
Part II: Statistics
2
Part II: Statistics
3
Chapter Five
Hypothesis Testing
(Statistical Inference: Part III Hypothesis Testing)
Part II: Statistics
1
In the previous chapter, we introduced the point and interval
estimation of an unknown parameter(s), say and 2.
In this chapter, we consider scienti
MGMT 4210
Corporate Strategy
Prof. Pavel Zhelyazkov
14/11/2016
MGMT 4210 - Corporate Strategy - Prof. Pavel Zhelyazkov
1
The class at a glance: The AFI Framework
Focus of today
Analysis
Background topics
Implementation
14/11/2016
Formulation
MGMT 4210 - C
MGMT 4210
Corporate Strategy
Prof. Pavel Zhelyazkov
31/10/2016
MGMT 4210 - Corporate Strategy - Prof. Pavel Zhelyazkov
1
M&A and Strategic Alliances
31/10/2016
MGMT 4210 - Corporate Strategy - Prof. Pavel Zhelyazkov
2
Today we focus on how firms manage
ex
MATH 2411 - L2&3
Week 8, Fall 2012
TA: Willis
SOLUTIONS TO EXAMPLES
Example 1
In this question, we are given that the r.v. X follows N(50,
). We need to be careful that the
conventional notation of normal distribution is to write out the mean
question we
MATH2411 - L2 & L3
Extra Notes on Hypothesis Testing
TA: Willis
yp
g
Hypothesis Testing Process
Step 1: Define Hypothesis
The Null Hypothesis, H0
The Alternative Hypothesis, H1
Always contains the = sign
Never contains the = sign
Step 2: Collect Data and
MATH2411 - L2 & L3
Extra Notes on Hypothesis Testing
Page 1 of 6
TA: Willis
MATH2411 - L2 & L3
Extra Notes on Hypothesis Testing
Page 2 of 6
TA: Willis
MATH2411 - L2 & L3
Extra Notes on Hypothesis Testing
Page 3 of 6
TA: Willis
MATH2411 - L2 & L3
Extra No
MATH2411 - L2&3
Week 8, Fall 2012
TA: Willis
Example 1
Given that the r.v. X follows a normal distribution with = 50 and = 10. Find
the probability of X taking value between 45 and 62.
Example 2
Suppose that a particular company has a history of making er
Summary for Math2411 (Spring 2012)
1. Numerical and graphical tools to describe data
cfw_xi , i = 1, 2, ., n is a set of data with n data points, and cfw_x(i) , i = 1, 2, ., n is its corresponding ordered data
set, with x(i) as the ith smallest data point
FB2200 Management Sciences I
Topic 6: One-Sample Test Extra Exercise (t-test)
Q1.
You are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting
time at the drive-through window for branches in your geographical region, as mea
Def. 7.3 Unbiasedness
Unbiasedness of Point Estimator
The sample statistic is an unbiased estimator of
the population parameter if E( )= , where E( )
is the expected value of the sample statistic .
Note: The reason for using n-1 instead of n in the
denomi
Expectations
4.1
the Expectation of a Random Variable
Definition 4.1 Let X be a discrete random variable with probability mass function f . Its expectation (mean) is
X
E(X) =
xf (x).
x
Definition 4.2 Let X be a continuous random variable with probability
NEGOTIATING A JOB OFFER II
& NEGOTIATING VIA EMAIL
Prof. Stephen W. Nason
Professor of Business Management
Prof Stephen W. Nason All Rights Reserved
Negotiation Outline: Where are We Going?
Negotiation
Fundamentals
Processes
Nature of
Negotiation
Percept
CASCADE MANOR
Prof. Stephen W. Nason
Professor of Business Practice
Prof Stephen W. Nason All Rights Reserved
Negotiation Outline: Where are We Going?
Negotiation
Fundamentals
Processes
Contexts
Remedies
Nature of
Negotiation
Perception
& Biases
Salary
N
VIKING INVESTMENTS:
DISPUTES & VIDEO ANALYSIS
Prof. Stephen W. Nason
Professor of Business Practice
Prof Stephen W. Nason All Rights Reserved
What is different about Viking?
Complicated
Big Power Difference
Dispute:
A claim has been made by one party
MGMT 3140
NEGOTIATION
Prof Stephen W. Nason
PhD
Professor of Business Practice
Prof Stephen W. Nason All Rights Reserved
1
SESSION 1
NEGOTIATION INTRODUCTION
Prof Stephen W. Nason All Rights Reserved
2
Who Likes Negotiating?
Why is Negotiation Important
MGMT 4210
Corporate Strategy
Prof. Pavel Zhelyazkov
19/10/2016
MGMT 4210 - Corporate Strategy - Prof. Pavel Zhelyazkov
1
Corporate Strategy
19/10/2016
MGMT 4210 - Corporate Strategy - Prof. Pavel Zhelyazkov
2
Next three lectures will be focused on
corpora