semester 2018 (aug dec) - kasetsart universityanan/myhomepage/wp-content/...anan phonphoem, dept.of...
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Department of Computer Engineering, Faculty of Engineering,Kasetsart University, THAILAND
1st Semester 2018 (Aug – Dec)
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Midterm Exam: 40 %
Final Exam: 40 %
Homework: 10 %
Assignment: 10 %
2Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University
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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
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• 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
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• 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
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⚫ Make-up exam will only be provided only for
restrict circumstances (severe illness)
6Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University
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Assoc. Prof. Anan Phonphoem, Ph.D.
Department of Computer Engineering, Faculty of Engineering,
Kasetsart University, THAILAND
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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
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⚫ 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]
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⚫ Definition⚫ Logic of probability
⚫ Axiom⚫ The truth: no proof needed (3)
⚫ Theorem⚫ Derived from definition and axiom
⚫ Proofed by definition, axiom, and other Theorems
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⚫ 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
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• 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
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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
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• 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
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Universal Set “S”
• Set (all possible members)
• By definition: Every set is subset of S
Null Set “”
• Empty set
• By definition: A
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• 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
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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
Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University
P = Q if and only if (iff) P Q and Q P
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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/
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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)
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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/
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• 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
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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.
Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University
LDDLL
LLLDL
DLLLD
2
5
1
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• 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
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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/
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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 …
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• 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}
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• 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}
Anan Phonphoem, Dept.of Computer Engineering, Kasetsart University
https://www.123rf.com/
P[E1] = 3/10
P[E2] = 5/10 = 1/2
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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]
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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] =
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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]
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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]
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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/