Semester 2018 (Aug Dec) - Kasetsart Universityanan/myhomepage/wp-content/...Anan Phonphoem, Dept.of...

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.

4Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

• 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.

5Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

⚫ Make-up exam will only be provided only for

restrict circumstances (severe illness)

6Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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

8Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

⚫ 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]

9Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

⚫ Definition⚫ Logic of probability

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

⚫ Theorem⚫ Derived from definition and axiom

⚫ Proofed by definition, axiom, and other Theorems

10Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

⚫ 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

11Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

• 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

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

• 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: ↔ ⇔ ≡

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University 14

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

15Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

• John Venn (1834 –1923), was a

British logician, and philosopher.

• Set Relations

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S S

A

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

http://en.wikipedia.org/

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A B

A B

AcAB

AB

AcA

ABA - B

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

19

(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

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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?

21Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University 22

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-

Mission: Impossible –

Rogue Nation

2015 150 687 A-

Mission: Impossible –

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

23Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

Same Procedure but different Observations → Different Experiments

25

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.

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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

26Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

29

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 …

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

• 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}

30Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

• 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”

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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Set Algebra Probability

Set Event

Universal set Sample space

Element Outcome

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

33

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}

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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]

34Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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] =

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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]

Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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]

37Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

The followings are not easy:

• From practical problem, model the experiment

carefully

• Derive the correct sample space

• Exam & Homework !!!

38Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University

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