SlideShare uma empresa Scribd logo
1 de 45
Baixar para ler offline
PROBABILITY – CONCEPTS OVERVIEW,[object Object],Posterior Probability,[object Object],[A revised probability based on additional information],[object Object],A value between 0 and 1, inclusive, describing the relative possibility [chance or likelihood) an event to occur,[object Object],Bayes’ Theorem,[object Object],Definition,[object Object],Terms,[object Object],Approaches,[object Object],Experiment, event, outcome, permutations, and combinations,[object Object],Subjective,[object Object],PROBABILITY,[object Object],Objective,[object Object],Multiplication [x],[object Object],1. Special Rule,[object Object],P(A and B) = P(A)P(B),[object Object],2. General Rule,[object Object],P(A and B) = P(A)P(B/C),[object Object],P(A and B and C) = P(A)P(P/A)P(C/A and B),[object Object],Rules,[object Object],Addition [ + ],[object Object],1. Mutually exclusive [only one event can occur],[object Object],P(A or B ) = P(A)+P(B),[object Object],2.Inclusive [both may occur],[object Object],P(A or B) = P(A) +P(B) –P(A and B),[object Object],AA,[object Object],AA,[object Object],AA,[object Object],AA,[object Object]
Chapter Five,[object Object],A Survey of Probability Concepts,[object Object],GOALS,[object Object],When you have completed this chapter, you will be able to:,[object Object],ONEDefine probability.,[object Object],TWODescribe the classical, empirical, and subjective approaches to probability.,[object Object],THREEUnderstand the terms: experiment, event, outcome, permutations, and combinations.,[object Object],Goals,[object Object]
Chapter Five  continued,[object Object],A Survey of Probability Concepts,[object Object],GOALS,[object Object],When you have completed this chapter, you will be able to:,[object Object],FOURDefine the terms: conditional probability and joint probability.,[object Object],FIVECalculate probabilities applying the rules of addition and the rules of multiplication.,[object Object],SIXUse a tree diagram to organize and compute probabilities.,[object Object],SEVENCalculate a probability using Bayes’ theorem.,[object Object],Goals,[object Object]
PROBABILITY – CONCEPTS OVERVIEW,[object Object],Posterior Probability,[object Object],[A revised probability based on additional information],[object Object],A value between 0 and 1, inclusive, describing the relative possibility [chance or likelihood) an event to occur,[object Object],Bayes’ Theorem,[object Object],Definition,[object Object],Terms,[object Object],Approaches,[object Object],Experiment, event, outcome, permutations, and combinations,[object Object],Subjective,[object Object],PROBABILITY,[object Object],Objective,[object Object],Multiplication [x],[object Object],1. Special Rule,[object Object],P(A and B) = P(A)P(B),[object Object],2. General Rule,[object Object],P(A and B) = P(A)P(B/C),[object Object],P(A and B and C) = P(A)P(P/A)P(C/A and B),[object Object],Rules,[object Object],Addition [ + ],[object Object],1. Mutually exclusive [only one event can occur],[object Object],P(A or B ) = P(A)+P(B),[object Object],2.Inclusive [both may occur],[object Object],P(A or B) = P(A) +P(B) –P(A and B),[object Object],AA,[object Object],AA,[object Object],AA,[object Object],AA,[object Object]
DEFINITION OF PROBABILITY,[object Object],A value between 0 and 1, inclusive, describing the relative possibility [chance or likelihood) an event to occur,[object Object],EXAMPLE:,[object Object],Toasting of a coin  A = Head , B = Tail,[object Object],P(A) = Probability of getting “Head” = ½ = 0.5,[object Object],P(B) = Probability of getting “Tail” = ½ - 0.5              P(A or B ) = ………………? =  …….?,[object Object],Note : Mutually Exclusive events = Head occurs Tail cannot occurs,[object Object]
DEFINITION OF PROBABILITY,[object Object],A value between 0 and 1, inclusive, describing the relative possibility [chance or likelihood) an event to occur,[object Object],EXAMPLE:,[object Object],Company A  and Company is Competing for a tender to be awarded by KUIS.,[object Object],P(A) = Probability of Company A getting  the tender = ……… ?,[object Object],P(B) = Probability of Company B getting  the tender = ………  ?         ,[object Object],P(A or B ) =  Probability of Company A or Company getting the tender = ………………? =  …….?,[object Object],Note : Mutually Exclusive events = Head occurs Tail cannot occurs,[object Object]
Definitions  continued,[object Object],There are three definitions of probability: classical, empirical, and subjective. ,[object Object],Subjectiveprobability is based on whatever information is available.,[object Object],The Classical definition applies when there are n equally likely outcomes.,[object Object],The Empirical definition applies when the number of times the event happens is divided by the number of observations.,[object Object]
Movie,[object Object]
An Outcome is the particular result of an experiment.,[object Object],Experiment:  A fair die is cast.,[object Object],Possible outcomes:  The numbers 1, 2, 3, 4, 5, 6 ,[object Object],An Event is the collection of one or more outcomes of an experiment.,[object Object],One possible event:  The occurrence of an even number.  That is, we collect the outcomes 2, 4, and 6.,[object Object],Definitions continued,[object Object]
Events are Mutually Exclusive if the  occurrence of any one event means that none of the others can occur at the same time.,[object Object],Events are Independent if the occurrence of one event does not affect the occurrence of another.  ,[object Object],Independence:  Rolling a 2 on the first throw does not influence the probability of a 3 on the next throw.  It is still a one in 6 chance.,[object Object],Mutually exclusive: Rolling a 2 precludes rolling a 1, 3, 4, 5, 6 on the same roll.,[object Object],Mutually Exclusive Events,[object Object]
Events are Collectively Exhaustive if at least one of the events must occur when an experiment is conducted.,[object Object],Collectively Exhaustive Events,[object Object]
This is an example of the empirical definition of probability.,[object Object],[object Object],Throughout his teaching career Mr. Shayaa Othman has awarded 186 A’s out of 1,200 students.   What is the probability that a student in her section this semester will receive an A?,[object Object],Example 2,[object Object]
Examples of subjective probability are:,[object Object],estimating the probability the Washington  Redskins will win the Super Bowl this year.,[object Object],estimating the probability mortgage rates for home loans will top 8 percent.,[object Object],Subjective Probability,[object Object]
If two events,[object Object], A and B are mutually exclusive, the,[object Object],Special Rule of Addition states that the ,[object Object],Probability of A or B occurring equals the sum of their respective probabilities. ,[object Object],P(A or B) = P(A) + P(B),[object Object],Basic Rules of Probability,[object Object]
MALAYSIAN AIRLINE [MAS] recently supplied the following information on their commuter flights from Singapore  to Kuala Lumpur:,[object Object],Example 3,[object Object]
If A is the event that a flight arrives early, then P(A) = 100/1000 = .10.,[object Object],If B is the event that a flight arrives late, then P(B) = 75/1000 = .075.,[object Object],The probability that a flight is either early or late is:,[object Object],P(A or B) = P(A) + P(B) = .10 + .075 =.175.,[object Object],Example 3  continued,[object Object]
The Complement Rule is used to determine the probability of an event occurring by subtracting the probability of the event not occurring from 1.  ,[object Object],If P(A) is the probability of event A and P(~A) is the complement of A,  ,[object Object],P(A) + P(~A) = 1 or    P(A) = 1 - P(~A).,[object Object],The Complement Rule,[object Object]
A Venn Diagram illustrating the complement rule would appear as:,[object Object],A,[object Object],~A,[object Object],The Complement Rule continued,[object Object]
Recall example 3. Use the complement rule to find the probability of an early (A) or a late (B) flight,[object Object],If C is the event that a flight arrives on time, then P(C) = 800/1000 = .8.,[object Object],If D is the event that a flight is canceled, then ,[object Object],P(D) = 25/1000 = .025.,[object Object],Example 4,[object Object]
P(A or B) 	= 1 - P(C or D) ,[object Object],		= 1 - [.8 +.025] ,[object Object],		=.175,[object Object],D,[object Object],.025,[object Object],C,[object Object],.8,[object Object],~(C or D) = (A or B),[object Object],              .175,[object Object],Example 4  continued,[object Object]
If A and B are two events that are not mutually exclusive, then P(A or B) is given by the following formula:,[object Object],P(A or B) = P(A) + P(B) - P(A and B),[object Object],The General Rule of Addition,[object Object]
The Venn Diagram illustrates this rule:,[object Object],B,[object Object],A and B,[object Object],A,[object Object],The General Rule of Addition,[object Object]
In a sample of 500 students, 320 said they had a stereo, 175 said they had a TV, and 100 said they had both.  5 said they had neither.,[object Object],TV,[object Object],175,[object Object],Both,[object Object], 100,[object Object],Stereo,[object Object],   320,[object Object],EXAMPLE 5,[object Object]
If a student is selected at random, what is the probability that the student has only a stereo or TV? What is the probability that the student has both a stereo and TV?,[object Object],P(S or TV) = P(S) + P(TV) - P(S and TV),[object Object],		 = 320/500 + 175/500 – 100/500,[object Object],		= .79.,[object Object],P(S and TV) = 100/500,[object Object],		   =  .20			,[object Object],Example 5 continued,[object Object]
A Joint Probability measures the likelihood that two or more events will happen concurrently.   ,[object Object],An example would be the event that a student has both a stereo and TV in his or her dorm room.,[object Object],Joint Probability,[object Object]
The Special Rule of Multiplication requires that two events A and B are independent.,[object Object],[object Object]
This rule is written:    P(A and B) = P(A)P(B)Special Rule of Multiplication,[object Object]
Ahmad owns two stocks, PROTON and Telekom Malaysia (TM).  The probability that PROTON stock will increase in value next year is .5 and the  probability that TM stock will increase in value next year is .7.  Assume the two stocks are independent.  What is the probability that both stocks will increase in value next year?,[object Object],P(PROTON and TM) = (.5)(.7) = .35,[object Object],Example 6,[object Object]
P(at least one) ,[object Object],= P(PROTON but not TM) ,[object Object],+ P(TM but not PROTON) ,[object Object],+ P(PROTON and TM),[object Object],   (.5)(1-.7) ,[object Object],+ (.7)(1-.5) ,[object Object],+ (.7)(.5) ,[object Object],= .85,[object Object]
A Conditional Probability is the probability of a particular event occurring, given that another event has occurred.,[object Object],The probability of event A occurring given that the event B has occurred is written P(A|B).,[object Object],Conditional Probability,[object Object]
The General Rule of Multiplication is used to find the joint probability that two events will occur.,[object Object],It states that for two events A and B, the joint probability that both events will happen is found by multiplying the probability that event A will happen by the conditional probability of B given that A has occurred.,[object Object],General Multiplication Rule,[object Object]
The joint probability, ,[object Object],P(A and B), is given by the following formula:  ,[object Object],P(A and B) = P(A)P(B/A)                          			or                                                           P(A and B) = P(B)P(A/B),[object Object],General Multiplication Rule,[object Object]
The Dean of the School of Business at INSANIAH University college collected the following information about undergraduate students in her college:,[object Object],Example 7,[object Object]
If a student is selected at random, what is the probability that the student is a female (F) accounting major (A)?  ,[object Object],P(A and F) = 110/1000.,[object Object],Given that the student is a female, what is the probability that she is an accounting major? 	,[object Object],P(A|F) = P(A and F)/P(F),[object Object],= [110/1000]/[400/1000] = .275,[object Object],Example 7  continued,[object Object]
A Tree Diagram is useful for portraying conditional and joint probabilities.  It is particularly useful for analyzing business decisions involving several stages.,[object Object],[object Object],Tree Diagrams,[object Object]
R2,[object Object],6/11,[object Object],R1,[object Object],7/12,[object Object],B2,[object Object],5/11,[object Object],R2,[object Object],7/11,[object Object],B1,[object Object],5/12,[object Object],B2,[object Object],4/11,[object Object],Example 8  continued,[object Object]
Bayes’ Theorem is a method for revising a probability given additional information.,[object Object],It is computed using the following formula:,[object Object],Bayes’ Theorem,[object Object]
Duff Cola Company recently received several complaints that their bottles are under-filled. A complaint was received today but the production manager is unable to identify which of the two Springfield plants (A or B) filled this bottle.  What is the probability that the under-filled bottle came from plant A?,[object Object],Example 9,[object Object]
The following table summarizes the Duff production experience.  ,[object Object],Example 9  continued,[object Object]
The likelihood the bottle was filled in Plant A is reduced from .55 to .4783.  ,[object Object],Example 9 continued,[object Object]
The Multiplication Formula  indicates that if there are m ways of doing one thing and n ways of doing another thing, there are m xn ways of doing both.,[object Object],Example 10: Dr. Fauzi has 10 shirts and 8 ties.  How many shirt and tie outfits does he have? ,[object Object],(10)(8) = 80,[object Object],Some Principles of Counting,[object Object]
A Permutation is any arrangement of r objects selected from n possible objects.,[object Object],Note: The order of arrangement is important in permutations.,[object Object],Some Principles of Counting,[object Object]
ACombination is the number of ways to choose r objects from a group of n objects without regard to order.,[object Object],Some Principles of Counting,[object Object]
There are 12 players on the Muar High School basketball team.  Coach Ahmad must pick 5 players among the twelve on the team to comprise the starting lineup.  How many different groups are possible?  (Order does not matter.),[object Object]
Suppose that in addition to selecting the group, he must also rank each of the players in that starting lineup according to their ability (order matters).    ,[object Object]

Mais conteúdo relacionado

Mais procurados

Theorems And Conditional Probability
Theorems And Conditional ProbabilityTheorems And Conditional Probability
Theorems And Conditional ProbabilityDataminingTools Inc
 
Probability&Bayes theorem
Probability&Bayes theoremProbability&Bayes theorem
Probability&Bayes theoremimran iqbal
 
introduction to probability
introduction to probabilityintroduction to probability
introduction to probabilitylovemucheca
 
Lecture: Joint, Conditional and Marginal Probabilities
Lecture: Joint, Conditional and Marginal Probabilities Lecture: Joint, Conditional and Marginal Probabilities
Lecture: Joint, Conditional and Marginal Probabilities Marina Santini
 
Stat lesson 4.2 rules of computing probability
Stat lesson 4.2 rules of computing probabilityStat lesson 4.2 rules of computing probability
Stat lesson 4.2 rules of computing probabilitypipamutuc
 
Conditional probability, and probability trees
Conditional probability, and probability treesConditional probability, and probability trees
Conditional probability, and probability treesGlobal Polis
 
Complements conditional probability bayes theorem
Complements  conditional probability bayes theorem  Complements  conditional probability bayes theorem
Complements conditional probability bayes theorem Long Beach City College
 
Basic probability concept
Basic probability conceptBasic probability concept
Basic probability conceptMmedsc Hahm
 
Probability Theory
Probability TheoryProbability Theory
Probability TheoryParul Singh
 
Mathematics for Language Technology: Introduction to Probability Theory
Mathematics for Language Technology: Introduction to Probability TheoryMathematics for Language Technology: Introduction to Probability Theory
Mathematics for Language Technology: Introduction to Probability TheoryMarina Santini
 
Probability Concepts Applications
Probability Concepts  ApplicationsProbability Concepts  Applications
Probability Concepts Applicationsguest44b78
 
Basic concept of probability
Basic concept of probabilityBasic concept of probability
Basic concept of probabilityIkhlas Rahman
 
Chapter 4 260110 044531
Chapter 4 260110 044531Chapter 4 260110 044531
Chapter 4 260110 044531guest25d353
 

Mais procurados (20)

Theorems And Conditional Probability
Theorems And Conditional ProbabilityTheorems And Conditional Probability
Theorems And Conditional Probability
 
Probability Theory
Probability Theory Probability Theory
Probability Theory
 
Basic concepts of probability
Basic concepts of probability Basic concepts of probability
Basic concepts of probability
 
Probability
ProbabilityProbability
Probability
 
Probability&Bayes theorem
Probability&Bayes theoremProbability&Bayes theorem
Probability&Bayes theorem
 
introduction to probability
introduction to probabilityintroduction to probability
introduction to probability
 
Unit 1-probability
Unit 1-probabilityUnit 1-probability
Unit 1-probability
 
Lecture: Joint, Conditional and Marginal Probabilities
Lecture: Joint, Conditional and Marginal Probabilities Lecture: Joint, Conditional and Marginal Probabilities
Lecture: Joint, Conditional and Marginal Probabilities
 
Stat lesson 4.2 rules of computing probability
Stat lesson 4.2 rules of computing probabilityStat lesson 4.2 rules of computing probability
Stat lesson 4.2 rules of computing probability
 
Conditional probability, and probability trees
Conditional probability, and probability treesConditional probability, and probability trees
Conditional probability, and probability trees
 
Complements conditional probability bayes theorem
Complements  conditional probability bayes theorem  Complements  conditional probability bayes theorem
Complements conditional probability bayes theorem
 
Laws of probability
Laws of probabilityLaws of probability
Laws of probability
 
Basic probability concept
Basic probability conceptBasic probability concept
Basic probability concept
 
Probability Theory
Probability TheoryProbability Theory
Probability Theory
 
Mathematics for Language Technology: Introduction to Probability Theory
Mathematics for Language Technology: Introduction to Probability TheoryMathematics for Language Technology: Introduction to Probability Theory
Mathematics for Language Technology: Introduction to Probability Theory
 
Basic concepts of probability
Basic concepts of probabilityBasic concepts of probability
Basic concepts of probability
 
Bayes Theorem
Bayes TheoremBayes Theorem
Bayes Theorem
 
Probability Concepts Applications
Probability Concepts  ApplicationsProbability Concepts  Applications
Probability Concepts Applications
 
Basic concept of probability
Basic concept of probabilityBasic concept of probability
Basic concept of probability
 
Chapter 4 260110 044531
Chapter 4 260110 044531Chapter 4 260110 044531
Chapter 4 260110 044531
 

Destaque

SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENT USING INTEGRATED BIO...
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENTUSING INTEGRATED BIO...SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENTUSING INTEGRATED BIO...
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENT USING INTEGRATED BIO...SAJJAD KHUDHUR ABBAS
 
Episode 66 : Renewable Energy Technologies
Episode 66 :  Renewable Energy TechnologiesEpisode 66 :  Renewable Energy Technologies
Episode 66 : Renewable Energy TechnologiesSAJJAD KHUDHUR ABBAS
 
Episode 13 : Research Methodology ( Part 3 )
Episode 13 :  Research Methodology ( Part 3 )Episode 13 :  Research Methodology ( Part 3 )
Episode 13 : Research Methodology ( Part 3 )SAJJAD KHUDHUR ABBAS
 
Episode 58 : Tools Integration Examples
Episode 58 :  Tools Integration ExamplesEpisode 58 :  Tools Integration Examples
Episode 58 : Tools Integration ExamplesSAJJAD KHUDHUR ABBAS
 
Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bio...
Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bio...Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bio...
Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bio...SAJJAD KHUDHUR ABBAS
 
‘Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bi...
‘Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bi...‘Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bi...
‘Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bi...SAJJAD KHUDHUR ABBAS
 
Episode 61 : MATERIAL BALANCE FOR REACTING SYSTEM
Episode 61 : MATERIAL BALANCE FOR REACTING SYSTEM Episode 61 : MATERIAL BALANCE FOR REACTING SYSTEM
Episode 61 : MATERIAL BALANCE FOR REACTING SYSTEM SAJJAD KHUDHUR ABBAS
 
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENT USING INTEGRATED BIO...
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENTUSING INTEGRATED BIO...SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENTUSING INTEGRATED BIO...
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENT USING INTEGRATED BIO...SAJJAD KHUDHUR ABBAS
 
Episode 57 : Simulation for Design and Analysis
Episode 57 : Simulation for Design and AnalysisEpisode 57 : Simulation for Design and Analysis
Episode 57 : Simulation for Design and AnalysisSAJJAD KHUDHUR ABBAS
 

Destaque (20)

Research Methodology Lecture for Master & Phd Students
Research Methodology  Lecture for Master & Phd StudentsResearch Methodology  Lecture for Master & Phd Students
Research Methodology Lecture for Master & Phd Students
 
STATISTICS & MANAGERIAL ETHICS : OVERVIEW OF PROBLEMS AND TOTAL SOLUTIONS IN...
STATISTICS & MANAGERIAL ETHICS :  OVERVIEW OF PROBLEMS AND TOTAL SOLUTIONS IN...STATISTICS & MANAGERIAL ETHICS :  OVERVIEW OF PROBLEMS AND TOTAL SOLUTIONS IN...
STATISTICS & MANAGERIAL ETHICS : OVERVIEW OF PROBLEMS AND TOTAL SOLUTIONS IN...
 
STRATEGIC MANAGEMENT: INCLUDING APPLICATION OF MAQASID AL-SHARIAH AS STRATEGI...
STRATEGIC MANAGEMENT: INCLUDING APPLICATION OF MAQASID AL-SHARIAH AS STRATEGI...STRATEGIC MANAGEMENT: INCLUDING APPLICATION OF MAQASID AL-SHARIAH AS STRATEGI...
STRATEGIC MANAGEMENT: INCLUDING APPLICATION OF MAQASID AL-SHARIAH AS STRATEGI...
 
Managing Waqf in Turkey and Malaysia for Educational Development. The Best Pr...
Managing Waqf in Turkey and Malaysia for Educational Development. The Best Pr...Managing Waqf in Turkey and Malaysia for Educational Development. The Best Pr...
Managing Waqf in Turkey and Malaysia for Educational Development. The Best Pr...
 
AN OVERVIEW OF ISLAMIC EDUCATION FOR HUMAN EXCELLENCE
AN OVERVIEW OF ISLAMIC EDUCATION FOR HUMAN EXCELLENCEAN OVERVIEW OF ISLAMIC EDUCATION FOR HUMAN EXCELLENCE
AN OVERVIEW OF ISLAMIC EDUCATION FOR HUMAN EXCELLENCE
 
Towards Strengthening Economics and Halal Spectrums
Towards Strengthening Economics  and Halal Spectrums Towards Strengthening Economics  and Halal Spectrums
Towards Strengthening Economics and Halal Spectrums
 
DATA COLLECTION IN RESEARCH
DATA COLLECTION IN RESEARCHDATA COLLECTION IN RESEARCH
DATA COLLECTION IN RESEARCH
 
RESEARCH WRITING - Apa References Style
RESEARCH WRITING - Apa References StyleRESEARCH WRITING - Apa References Style
RESEARCH WRITING - Apa References Style
 
MAPPiCXS : Teknik Berfikir Seperti Genius
MAPPiCXS : Teknik Berfikir Seperti GeniusMAPPiCXS : Teknik Berfikir Seperti Genius
MAPPiCXS : Teknik Berfikir Seperti Genius
 
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENT USING INTEGRATED BIO...
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENTUSING INTEGRATED BIO...SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENTUSING INTEGRATED BIO...
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENT USING INTEGRATED BIO...
 
Episode 66 : Renewable Energy Technologies
Episode 66 :  Renewable Energy TechnologiesEpisode 66 :  Renewable Energy Technologies
Episode 66 : Renewable Energy Technologies
 
Episode 13 : Research Methodology ( Part 3 )
Episode 13 :  Research Methodology ( Part 3 )Episode 13 :  Research Methodology ( Part 3 )
Episode 13 : Research Methodology ( Part 3 )
 
Episode 58 : Tools Integration Examples
Episode 58 :  Tools Integration ExamplesEpisode 58 :  Tools Integration Examples
Episode 58 : Tools Integration Examples
 
Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bio...
Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bio...Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bio...
Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bio...
 
‘Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bi...
‘Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bi...‘Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bi...
‘Sustainable Approach Of Recycling Palm Oil Mill Effluent Using Integrated Bi...
 
Episode 61 : MATERIAL BALANCE FOR REACTING SYSTEM
Episode 61 : MATERIAL BALANCE FOR REACTING SYSTEM Episode 61 : MATERIAL BALANCE FOR REACTING SYSTEM
Episode 61 : MATERIAL BALANCE FOR REACTING SYSTEM
 
Islamic Finance and Opportunities Projected to 2020
Islamic Finance and Opportunities Projected to 2020Islamic Finance and Opportunities Projected to 2020
Islamic Finance and Opportunities Projected to 2020
 
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENT USING INTEGRATED BIO...
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENTUSING INTEGRATED BIO...SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENTUSING INTEGRATED BIO...
SUSTAINABLE APPROACH OF RECYCLING PALM OIL MILL EFFLUENT USING INTEGRATED BIO...
 
Episode 57 : Simulation for Design and Analysis
Episode 57 : Simulation for Design and AnalysisEpisode 57 : Simulation for Design and Analysis
Episode 57 : Simulation for Design and Analysis
 
APPLICATION OF MAQASID AL SHARIAH IN STRATEGIC MANAGEMENT INCLUDING MAQASID A...
APPLICATION OF MAQASID AL SHARIAH IN STRATEGIC MANAGEMENT INCLUDING MAQASID A...APPLICATION OF MAQASID AL SHARIAH IN STRATEGIC MANAGEMENT INCLUDING MAQASID A...
APPLICATION OF MAQASID AL SHARIAH IN STRATEGIC MANAGEMENT INCLUDING MAQASID A...
 

Semelhante a Lecture on Statistics 1

Semelhante a Lecture on Statistics 1 (20)

Probability Concepts
Probability ConceptsProbability Concepts
Probability Concepts
 
Chapter 05
Chapter 05Chapter 05
Chapter 05
 
Lesson 5.ppt
Lesson 5.pptLesson 5.ppt
Lesson 5.ppt
 
CLO2-PPT2-Probability Addition Rules.pptx
CLO2-PPT2-Probability Addition Rules.pptxCLO2-PPT2-Probability Addition Rules.pptx
CLO2-PPT2-Probability Addition Rules.pptx
 
Probability.pptx
Probability.pptxProbability.pptx
Probability.pptx
 
Chapter 05
Chapter 05 Chapter 05
Chapter 05
 
Chap005Lind.ppt
Chap005Lind.pptChap005Lind.ppt
Chap005Lind.ppt
 
Bab 5.ppt
Bab 5.pptBab 5.ppt
Bab 5.ppt
 
Probability concepts for Data Analytics
Probability concepts for Data AnalyticsProbability concepts for Data Analytics
Probability concepts for Data Analytics
 
7-Experiment, Outcome and Sample Space.pptx
7-Experiment, Outcome and Sample Space.pptx7-Experiment, Outcome and Sample Space.pptx
7-Experiment, Outcome and Sample Space.pptx
 
Chapter6
Chapter6Chapter6
Chapter6
 
IPPTCh005.pptx
IPPTCh005.pptxIPPTCh005.pptx
IPPTCh005.pptx
 
G10 Math Q4-Week 1- Mutually Exclusive.ppt
G10 Math Q4-Week 1- Mutually Exclusive.pptG10 Math Q4-Week 1- Mutually Exclusive.ppt
G10 Math Q4-Week 1- Mutually Exclusive.ppt
 
MATHS_PROBALITY_CIA_SEM-2[1].pptx
MATHS_PROBALITY_CIA_SEM-2[1].pptxMATHS_PROBALITY_CIA_SEM-2[1].pptx
MATHS_PROBALITY_CIA_SEM-2[1].pptx
 
Probability
ProbabilityProbability
Probability
 
tps5e_Ch5_3.ppt
tps5e_Ch5_3.ppttps5e_Ch5_3.ppt
tps5e_Ch5_3.ppt
 
tps5e_Ch5_3.ppt
tps5e_Ch5_3.ppttps5e_Ch5_3.ppt
tps5e_Ch5_3.ppt
 
Chapter06
Chapter06Chapter06
Chapter06
 
Chapter 4 Probability Notes
Chapter 4 Probability NotesChapter 4 Probability Notes
Chapter 4 Probability Notes
 
3.2 probablity
3.2 probablity3.2 probablity
3.2 probablity
 

Mais de SHAYA'A OTHMAN MANAGEMENT & RESEARCH METHODOLOGY (6)

Research Strategies - Reference Note 1
Research Strategies - Reference Note 1Research Strategies - Reference Note 1
Research Strategies - Reference Note 1
 
Model Example of Research Proposal
Model Example of Research Proposal Model Example of Research Proposal
Model Example of Research Proposal
 
Note 4: Sample Research Paper APA Reference
Note 4: Sample Research Paper APA ReferenceNote 4: Sample Research Paper APA Reference
Note 4: Sample Research Paper APA Reference
 
Note 3. Qualitative Research Vs Quantitative Research
Note 3. Qualitative Research Vs Quantitative ResearchNote 3. Qualitative Research Vs Quantitative Research
Note 3. Qualitative Research Vs Quantitative Research
 
Note 2 writing a research
Note 2    writing a researchNote 2    writing a research
Note 2 writing a research
 
Note 1 : RESEARCH METHODOLOGY
Note 1 : RESEARCH METHODOLOGYNote 1 : RESEARCH METHODOLOGY
Note 1 : RESEARCH METHODOLOGY
 

Último

The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsEugene Lysak
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxDr. Santhosh Kumar. N
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxraviapr7
 
Easter in the USA presentation by Chloe.
Easter in the USA presentation by Chloe.Easter in the USA presentation by Chloe.
Easter in the USA presentation by Chloe.EnglishCEIPdeSigeiro
 
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptxSandy Millin
 
Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...raviapr7
 
Diploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfDiploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfMohonDas
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesCeline George
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxheathfieldcps1
 
HED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfHED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfMohonDas
 
In - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxIn - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxAditiChauhan701637
 
Ultra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxUltra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxDr. Asif Anas
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfTechSoup
 
How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17Celine George
 
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxPractical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxKatherine Villaluna
 
5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...CaraSkikne1
 
How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17Celine George
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice documentXsasf Sfdfasd
 
CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapitolTechU
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17Celine George
 

Último (20)

The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George Wells
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptx
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptx
 
Easter in the USA presentation by Chloe.
Easter in the USA presentation by Chloe.Easter in the USA presentation by Chloe.
Easter in the USA presentation by Chloe.
 
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
2024.03.23 What do successful readers do - Sandy Millin for PARK.pptx
 
Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...Patient Counselling. Definition of patient counseling; steps involved in pati...
Patient Counselling. Definition of patient counseling; steps involved in pati...
 
Diploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfDiploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdf
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 Sales
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptx
 
HED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfHED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdf
 
In - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxIn - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptx
 
Ultra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxUltra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptx
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
 
How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17
 
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxPractical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
 
5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...
 
How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice document
 
CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptx
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17
 

Lecture on Statistics 1

  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.
  • 24.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • 40.
  • 41.
  • 42.
  • 43.
  • 44.
  • 45.