7.VECTORSPACES
7.1DefinitionofaVectorSpace
Definition:A(real)vectorspaceisanonemptyset V ofelementsinwhich2operations
and aredefinedwiththefollowingproperties:
a. If , V then V .
1. = , , V
2. ( ) =
Rank
I.
Linear Combination of Vectors
If we have n vectors all of the same order, which we call a set of n vectors, , , , , then for scalars
1 , 2 , , ,
1 + 2 + +
is called a linear combination of th
School of Statistics
UNIVERSITY OF THE PHILIPPINES
STATISTICS 135
Matrix Theory for Statistics
1st Semester, AY 2017-2018
Instructor: Paolo Victor T. Redondo
Phone: 09178369622
Email: [email protected]
6.
6.1
LINEARSYSTEMS
Definitions
+ a 2 x 2 + . + a n x n = b , which expresses b in terms of the
variables x1 , x 2 ,., x n andtheconstants a1 , a 2 ,., a n ,iscalledalinearequation
in x1 , x 2 ,., x
1
1.1
INTRODUCTION
Algebra is mathematical shorthand for language, and matrices are
shorthand for algebra. A special value of matrices is that they enable many
mathematical operations, especially thos
5. INVERSEMATRICES
Division in the ordinary sense is undefined in matrix algebra. The expression
B
A
has no meaning when
A is a matrix. We deal with inverse matrices and use
1
them as multipliers, e.
Royell T. Guevarra
BSIT-ELT IVA
Assignment in IT 3
1.) 3D Basic Modeling
Basic Tools in 3D in AutoCAD
The most basic figure of the 3D concept is a cube, something like this:
A cube is a 2D face extrud
Chas Campbells Flywheel System.
Recently, Mr. Chas Campbell of Australia demonstrated electrical power gain with a flywheel system
which he
developed:
But what this diagram does not show, is that a co
E GOVERNMENT (LTO Land Transportation Office)
I.
Introduction
MISSION
Rationalize the land transportation services and facilities and to effectively
implement the various transportation laws, rules an
Ain't got a soapbox I can stand upon
But God gave me a stage, a guitar and a song
My daddy told me, "Son, don't you get involved in
Politics, religions, other peoples' quarrels"
[Pre-Chorus]
I'll pain
LORLIE ANN P. SONORON
BPE-SWM
WHAT?
The World Bank Group (WBG) (French: Groupe de la Banque mondiale)[5] is a family of five
international organizations that make leveraged loans to developing countri
Radio signals
- an overview of what radio signals are and the relationship between frequency and wavelength
Radio signals are used for a huge variety of tasks. Radio signals are used to carry radio
br
Stat 101 | 1718FirstSem | CAAAntonio
By the end of the chapter, the learner is expected
to be able
to differentiate percent and percentiles
to explain the relationship between quantiles
(percentiles
Sampling and Sampling Techniques
Stat101 | 1718FirstSem | CAAntonio
By the end of the chapter, the learner is expected to be
able
to differentiate between a census and a sampling survey
to understan
Organization
of
Data
Stat101 | 1718FirstSem | CAAntonio
Raw Data data in their original form
Array ordered arrangement of data according
to magnitude
Frequency Distribution way of summarizing
data by
POINTERS TO REVIEW
Descriptive vs. Inferential Statistics (identify if given study is an application of inferential or
descriptive)
Applications of Stat in your field (concrete application/s of Stat)
Collection of Data
Stat 101 | AY1718FirstSem | CAAAntonio
Learning Outcomes
By the end of the chapter, the learner is expected
to be able
to identify in what level of measurement variables
are measur
STATISTICS:
An Introduction
Stat 101 | AY1718FirstSem | CAAAntonio
Whats Stat?
Learning Outcomes
By the end of the chapter, the learner is expected to be able
to define Statistics completely
to iden
Measures of Central Tendency
Stat 101 | 1718FirstSem | CAAAntonio
By the end of the chapter, the learner is expected to
be able
to calculate using the summation operator
to be familiar with the prop
Measures of Skewness
and Kurtosis
By the end of the chapter, the learner is expected
to be able
to differentiate negative and positive skewness
to be familiar with the types of kurtosis
Consider the
Measures of Dispersion
Stat 101 | 1718 FirstSem | CAAAntonio
By the end of the chapter, the learner is expected to be
able
to explain the difference between measures of
absolute dispersion and measur
Presentation of Data
Stat101 | 1718FirstSem | CAAAntonio
It is important that we present the results
of our analysis in some form that will allow
us to reveal and highlight the important
information t
CHAP. 21
TECHNIQUES O F COUNTING
31
TREE DIAGRAMS
2.29.
Construct the tree diagram for the number of permutations of (a, b, c.
C
bac
a
b
bca
cab
a
cba
The six permutations are listed on the right of t
Coincidences, in general, are great
stumbling blocks in the way of that
class of thinkers who have been
educated to know nothing of
probabilities that theory to which
the most glorious objects of huma
Dont worry about failures, worry
about the chances you miss when
you dont even try.
Chapter 2
INTRODUCTION TO PROBABILITY
Motivation
We already introduced the field of probability theory during the Pa
Statistical thinking will one day be as
necessary for efficient citizenship as
the ability to read and write.
Chapter 1 DESCRIPTIVE STATISTICS
Motivation
Statistics is the perfect tool!
I keep saying