MA-2214
Data Analysis
Tandon School of
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TRIO Scholars Program
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1. Bernoulli
Binomial Probability Distribution
"Bi" means "two"(like a bicycle has two wheels) .
. so this is about things withtwo results.
Like Tossing a Coin,
MA-2214
Data Analysis
Tandon School of
Engineering
TRIO Scholars Program
Made By Haosen Zhao
1. Poisson Random Variable
Theprobability distribution of a Poisson random variableXrepresentng the number of
successes occurring in a given tme interval or a sp
MA-2214
Data Analysis
Tandon School of
Engineering
TRIO Scholars Program
Made By Haosen Zhao
1. Combinations &
Permutations
When the order doesn't mater, it is aCombination.
When the orderdoesmater it is aPermutation.
A Permutaton is anorderedCombinato
MA-2214
Data Analysis
Tandon School of
Engineering
TRIO Scholars Program
Made By Haosen Zhao
1. Random Variable
A Random Variable is a set ofpossible valuesfrom a random experiment.
Just like the weather tomorrow, the president after 4 years
Not Like a
MA-2214
Data Analysis
Tandon School of
Engineering
TRIO Scholars Program
Made By Haosen Zhao
1. Stem and Leaf Plot
Stem-and-leaf plots are a method for showing the frequency with which certain
classes of values occur.
For example: suppose you have the f
MA-2214
Data Analysis
Tandon School of
Engineering
TRIO Scholars Program
Made By Haosen Zhao
1. Set theory
The union of two sets is a new set that contains all of the elements that are in at
least one of the two sets. The union is writen asAB.
1. Set the
(1) Let X be a random variable with the p.d.f.
=
%& '
(
for 1 x 1.
Show your work when solving the following problems.
(a) Find P (X > 0.25).
(b) Find the mean () and the variable ( ) of X.
(c) Let 6 , ( , , (9 be a random sample of size 24 from the ab
(1) Let " , $ & be a random sample from the bi(1, p) distribution so that
Xi = 1 corresponds to a success with probability p and Xi = 0
corresponds to a failure with probability 1 p.
(a) What is the expected value and variance of Xi?
(b) What is the appro
MA-2214
Data Analysis
Tandon School of
Engineering
TRIO Scholars Program
Made By Haosen Zhao
1. T distribution
The foundation behind any hypothesis test is being able to take the test statistic
from a specific sample and place it within the context of a
1. In a United State election, a political analyst believes that if Democrats win
Florida, their probability of win the election is 0.9 and if they lose Florida, the
possibility of winning the election is 0.4. The analysis believes the possibility
of the
MA-2214
Data Analysis
Tandon School of
Engineering
TRIO Scholars Program
Made By Haosen Zhao
1. Interval Estimate
A Confdence Interval is arange of valueswe are fairly sure ourtrue valuelies
in.
1. Interval Estimate
Ex.
We measure the heights of40rando
(1) Suppose the FAA weighed a random sample of 20 airline passengers
during the summer and found their weights to have a sample mean of 170
pounds and sample standard deviation of 20 pounds. Assume the weight
distribution is approximately normal.
(a) Find
Nested Quantifiers
Section 1.5
Section Summary
Nested Quantifiers !
Order of Quantifiers!
Translating from Nested Quantifiers into English!
Translating Mathematical Statements into Statements
involving Nested Quantifiers.!
Translated English Sentence
Sets Cont.
Section 2.1
Set Equality
Definition: Two sets are equal if and only if they have
the same elements.
Therefore if A and B are sets, then A and B are equal if
and only if
We write A = B if A and B are equal sets.
cfw_1,3,5 = cfw_3, 5, 1
cfw_1,5
Inverse Functions
Definition: Let f be a bijection from A to B. Then the
inverse of f, denoted
, is the function from B to A
defined as!
No inverse exists unless f is a bijection. Why?!
Inverse Functions
A
a
f
B
V
b
W
c
d
A
B
a
V
b
W
c
X
Y
d
X
Y
Questions
Basic Structures: Sets,
Functions, Sequences, and
Sums
Chapter 2
Modification of the McGraw Hill Slides
Chapter Summary
Sets !
The Language of Sets!
Set Operations!
Set Identities!
Functions!
Types of Functions!
Operations on Functions!
Computabil
Introduction to Proofs
Section 1.7
Section Summary
Mathematical Proofs!
Forms of Theorems!
Direct Proofs!
Indirect Proofs!
Proof of the Contrapositive!
Proof by Contradiction
Proofs of Mathematical Statements
A proof is a valid argument that establ
The Foundations: Logic
and Proofs
Chapter 1, Part II: Predicate Logic
Modification of the McGraw Hill Slides
Predicates and
Quantifiers
Section 1.4
Section Summary
Predicates !
Variables!
Quantifiers!
Universal Quantifier!
Existential Quantifier!
Ne
The Foundations: Logic
and Proofs
Chapter 1, Part I: Propositional Logic
Modification of the McGraw Hill Slides
Chapter Summary
Propositional Logic!
! The Language of Propositions!
! Applications!
! Logical Equivalences
Predicate Logic!
! The Language o
Auctions: Travelexis
Prof. Stephen W. Nason
Professor of Business Practice
ProfStephenW.Nason AllRightsReserved
NegotiationOutline:WhereareWeGoing?
Negotiation
Fundamentals
Processes
Natureof
Perception
Negotiation
Distributive
Negotiations
Integrative
Ne
SESSION 2
INTEGRATIVE NEGOTIATIONS
Prof. Stephen W. Nason
Professor of Business Practice
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NegotiationOutline:WhereareWeGoing?
Negotiation
Fundamentals
Processes
Contexts
Remedies
Natureof
Negotiation
Perception
&Biases
NEGOTIATION FUNDAMENTALS
Prof Stephen W. Nason
Professor of Business Practice
ProfStephenW.Nason AllRightsReserved
BargainingZone:TexoilCase
Initialoffer
$?
Texoil
Buyer
Max
$500K
/
/
/
/
$553K
Min
Station
$?
OwnerSeller Initialoffer
NegotiationFundamenta
BROOKSIDE COMMUNITY HOSPITAL
VS. BLACK COMPUTER SYSTEMS
Prof. Stephen W. Nason
Professor of Business Practice
ProfStephenW.Nason AllRightsReserved
WhatisDifferentAboutBrooksidevs.BlackFrom
theOtherNegotiations?
Team:
PowerDifference:
Dispute:
Aclaimha
DISTRIBUTIVE NEGOTIATIONS:
THE COFFEE CONTRACT
Prof. Stephen NASON
Professor of Business Practice
Prof Stephen W. Nason All Rights Reserved
Succeeding in Negotiations
You will never lose if you understand
Reservation Point (Bottom Line)
Your BATNA (Bes
COALITIONS: HARBORCO
Prof. Stephen W. Nason
Professor of Business Practice
ProfStephenW.Nason AllRightsReserved
NegotiationOutline:WhereareWeGoing?
Negotiation
Fundamentals
Processes
Contexts
Remedies
Natureof
Negotiation
Perception
&Biases
Salary
Negotia
NEGOTIATION FUNDAMENTALS
Prof Stephen W. Nason
Professor of Business Practice
ProfStephenW.Nason AllRightsReserved
NegotiationOutline:WhereareWeGoing?
Negotiation
Fundamentals
Processes
Contexts
Remedies
Natureof
Negotiation
Perception
&Biases
Salary
Nego
CROSS-CULTURAL NEGOTIATIONS
Prof. Stephen W. Nason
Professor of Business Practice
ProfStephenW.Nason AllRightsReserved
NegotiationOutline:WhereareWeGoing?
Negotiation
Fundamentals
Processes
Contexts
Remedies
Natureof
Negotiation
Perception
&Biases
Salary
ELEC1010 Tutorial 4
1
Frequency Filter
Frequency Translation
Filter
Allows some frequencies of a signal to pass through and
block other frequencies of the signal.
In Frequency domain, the output spectrum Y is the
product of the filter characteristic H and
ELEC1010 Tutorial 6
1
Digitization
Sampling
Quantization
Digitization
Digital Signal: a set of sampled values in binary form as
bits.
Two main operations for digitization
1. Sampling:
Convert an analog signal into a list of numbers
Each number is one samp
ELEC1010 Tutorial 5
1
Analog Signals and Systems
Digital Signals and Systems
Binary Format
Binary Logic
Analogy Signals and Systems
Analog Signals
Continuous
Not countable
Have an infinite number of values
e.g. audio signal, visual signal, distance, time