Semester 2018 (Aug Dec) - Kasetsart Universityanan/myhomepage/wp-content/...Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University 3 Description Score (0 –1)0 –15 min

Department of Computer Engineering, Faculty of Engineering,Kasetsart University, THAILAND

1st Semester 2018 (Aug – Dec)

Midterm Exam: 40 %

Final Exam: 40 %

Homework: 10 %

Assignment: 10 %

2Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University 3

Description Score (0 – 1)

0 – 15 min 1

15.01 – 100 min (100 – MinLate)/100

> 100 min 0

If missing class

• with “letter of leave of absence in advanced”

• without “letter of leave of absence in advanced”

0.5

0

• Your Grade is based on the overall class performance.

• However, the cumulative score below 50% is considered as

fail (F).

• An “F” grade will be given to any form of cheating (for all

parties).

• You are not allowed to take a midterm exam if you miss

more than 2 lectures and also not allowed to take final exam

if you miss more than 4 lectures.


• All hard-copy assignments must be handed in at the beginning of the class (> 15 min. is considered late).

• For soft-copy will be timed by the local time stamp.

• No Late assignment will be graded.

• No credit for plagiarism and considered as cheating.

• No credit for copying homework or assignment (for all copies) and considered as cheating.


⚫ Make-up exam will only be provided only for

restrict circumstances (severe illness)


Assoc. Prof. Anan Phonphoem, Ph.D.

Department of Computer Engineering, Faculty of Engineering,

Kasetsart University, THAILAND

What will you think of about Probability?

• Physical PropertyExample: Tossing a dice, a coin, buying lottery

• KnowledgeExample: Earthquake in Thailand, Web page has been

hacked, Trapped in cave


⚫ Situation cannot exactly be replicated

⚫ Cooking

⚫ Producing Memory chip, CPU, Harddisk

⚫ But not chaotic

⚫ If perform many experiments, there should be a pattern

⚫ Tossing a coil 100 times

⚫ Probability Value

⚫ [0,1]


⚫ Definition⚫ Logic of probability

⚫ Axiom⚫ The truth: no proof needed (3)

⚫ Theorem⚫ Derived from definition and axiom

⚫ Proofed by definition, axiom, and other Theorems


⚫ Set: Basic mathematics for probability

⚫ Definition

Set: group of interesting things

Element: members of Set

⚫ Set & Element

a A a is an element of set A (set inclusion)

b B b is not an element of set B


• T = {Notebook, I-Phone, Wallet, Keys}

• R = {x2+1 | x = 1, 3 , 5, …}

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Set Name composes of Set member

{on Left side (member of Set) | condition to be members}

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

13

R = {x2+1 | x = 1, 3, 5, …}

I = {Integer Number}

R I

Set Equality

A = B if and only if (iff) A B and B A

Subset

A B set A is a subset of set B


• Bi-conditional logical connective between

statements

• The truth of either one of the connected

statements requires the truth of the other

• i.e., either both statements are true, or both are false

• XNOR gate (opposite of XOR)

• Symbol: ↔ ⇔ ≡


p q p↔ q

T T T

T F F

F T F

F F T

Definition from: http://en.wikipedia.org/wiki/If_and_only_if

Set Equality A = B if and only if (iff) A B and B A

Universal Set “S”

• Set (all possible members)

• By definition: Every set is subset of S

Null Set “”

• Empty set

• By definition: A


• John Venn (1834 –1923), was a

British logician, and philosopher.

• Set Relations

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S S

A


http://en.wikipedia.org/

http://en.wikipedia.org/wiki/File:John_Venn.jpg

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A B

A B

AcAB

AB

AcA

ABA - B


A B

C

A B C

1. Mutually Exclusive

Ai Aj = for i j

For only 2 sets, A B =

called Disjoint

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A1

A2

A3

A1

A2

Ui = 1

n

Ai = S

2. Collectively Exhaustive

A1 A2 … An = S


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(A B)c = Ac Bc

Proof: (A B)c Ac Bc and Ac Bc (A B)c

x (A B)c

→x A B

→x A and x B

→x Ac and x Bc

→x Ac Bc

x Ac Bc

→x Ac and x Bc

→x A and x B

→x A B

→x (A B)c


P = Q if and only if (iff) P Q and Q P

What is an Experiment?

• Method for finding some facts/conclusions

Give an example?

• For movie “Mission Impossible - Fallout”, is it fun?


http://time.com/5349500/mission-impossible-fallout/


Film Year Budget

(M$)

Box off.

gross

(M $)

Cimema

Score

Mission: Impossible 1996 80 458 B+

Mission: Impossible 2 2000 125 546 B

Mission: Impossible III 2006 150 398 A-

Mission: Impossible –

Ghost Protocol

2011 145 695 A-


Rogue Nation

2015 150 687 A-


Fallout

2018 178 330(1 month)

A

https://upload.wikimedia.org/wikipedia/en/3/3c/Missionimpossible

blurayboxset.jpghttps://en.wikipedia.org/wiki/Mission:_Impossible_(film_series)

What is an Experiment? • Method for finding some facts/conclusions

Give an example?• For movie “Mission Impossible - Fallout”, is it fun?• Stand in front of the theatre• Ask audiences, fun or not?

Composition of an experiment• Procedure• Observation

Why experiment is needed?• Uncertainty


https://variety.com/2018/film/reviews/mission-impossible-fallout-review-

1202872043/

• Concern about movie “Mission Impossible - Fallout” experiment

• Should I ask man, women, or teenager?

• Experience of the audiences

• Knowledge of the audiences

• Complicated experiment →need Model

• Real experiments: too complicate

• Capture only the important part

• Model Example:

• Treat all audiences the same

• Answer will only be like/dislike

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http://www.comic-spass.de/story-en.html


Same Procedure but different Observations → Different Experiments

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Example:

1. Stand in front of the show “Mission Impossible”

and ask 5 people,

Observe the # of people who like the show.

2. Stand in front of the show “Mission Impossible”

and ask 5 people,

Observe the sequence of people who like the show.


LDDLL

LLLDL

DLLLD

2

5

1

• Outcome

• Any possible observation

• Sample Space

• Finest-grain: each outcome is different

• Mutually exclusive: if one outcome occurs, other will not occur

• Collectively exhaustive: every outcome must be in the sample

space

• Event

• Set of outcomes (Must know all outcomes )

• Event Sample Space


Outcomes:number = 0,1,2,3,4,5,6,7,8,9

Sample space:S = {0,1,2,…,9}

Event examples:E1 = {number < 3} = {0,1,2}E2 = {number is odd} = {1,3,5,7,9}

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For an experiment:

Press a number on the ATM keypad,

observe the number was pressed


https://www.123rf.com/

Sample Space• Finest-grain, Mutually exclusive, and Collectively exhaustive

• Members are outcomes

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Definition: Event Space* Mutually exclusive

* Collectively exhaustive event

• Members are events


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Theorem:

For an event space B = {B1, B2, …}

and any event A in the S,

Let Ci = A ∩ Bi for i ≠ j,

the events Ci and Cj are mutually exclusive

and A = C1 U C2 U …


• Experiment:• Receive 3-bit data

• Examine the data bit in order and observe either data bit is “1” or “0”

• Sample space:• S = {000, 001, 010, 011, 100, 101, 110, 111 }

• Bi = {Outcomes with i Zeros} For i = 0,1,2,3

• B2 = {001, 010, 100}

• Event space B = {B0, B1, B2, B3}


• S = {000, 001, 010, 011, 100, 101, 110, 111 }

• Let X = {outcomes < 2 Zeros}

• X = {011, 101, 110, 111 }

• X = (X∩B0)U(X∩B1)U(X∩B2)U(X∩B3)

= B0 U B1 U U

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Bi X for i = 0 and 1

Event “< 2 Zeros” = “no Zero” U “1 Zero”


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Set Algebra Probability

Set Event

Universal set Sample space

Element Outcome


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P[☺]

is a function that maps event

in the sample space to real numberFrom experiment: Press a number on the ATM keypadOutcomes:

number = 0,1,2,3,4,5,6,7,8,9

Sample space:S = {0,1,2,…,9}

Event examples:E1 = {number < 3} = {0,1,2}E2 = {number is odd} = {1,3,5,7,9}


https://www.123rf.com/

P[E1] = 3/10

P[E2] = 5/10 = 1/2

Axiom 1: For any event A, P[A] 0

Axiom 2: P[S] = 1

Axiom 3: For events A1, A2,…, An

of mutual exclusive events

P[A1A2…An] = P[A1]+P[A2]+…+P[An]


Theorem: If A and B are disjoint, then

P[A B] = P[A] + P[B]

Theorem: If B = B1 B2…Bn and

BiBj = for i j, then

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i = 1

n

P[Bi]P[B] =


Theorem: For an experiment with sample space

S={s1,…, sn} if each outcome is equally likely,

P[si] = 1/n 1 i n

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n repetitions (trials), The number of Event A occurs: NA(n)

limn → ∞ n

NA(n)= P[A]


Theorem:

• P[] = 0

• P[Ac] = 1 - P[A]

• For any A and B (not necessary disjoint)

P[A B] = P[A] + P[B] – P[AB]

• If A B , then P[A] P[B]


The followings are not easy:

• From practical problem, model the experiment

carefully

• Derive the correct sample space

• Exam & Homework !!!


http://mikeiamele.com/make-life-easy/

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Semester 2018 (Aug Dec) - Kasetsart Universityanan/myhomepage/wp-content/...Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University 3 Description Score (0 –1)0 –15 min