Makalah Statistika dan Probabilitas. LAPORAN STATISTIKA DAN PROBABILITAS “Aplikasi Tabel Kontingensi Satu Arah & Tabel Kontingensi Dua Arah”. Tugas Probabilitas Dan Statistika - Download as Word Doc (.doc /.docx), PDF File (.pdf), Text File (.txt) or read online. MAKALAH iNTROSPEKTIF.docx.
Penggambaran Data dengan Grafik. 1. Introduction to Probability and Statistics Eleventh Edition Robert J. Beaver. Barbara M. Beaver. William Mendenhall Presentation designed and written by: Barbara M.
Beaver with minor change by Joon Jin Song. Introduction to Probability and Statistics Eleventh Edition Chapter 1 Describing Data with Graphs Some graphic screen captures from Seeing Statistics ® Some images © 2001-(current year) www.arttoday.com.
Syllabus Instructor: Dr. Joon Jin Song E-mail: [email protected] Office Hours: TR 3:00-5:00 or by appointment Website: Office: LGRT 1434, phone: 577-0255 Grader: TBA Text: Introduction to Probability and Statistics 11th ed., W. Mendenhall, R. Beaver, and B. Syllabus Required Software Tools MINITAB (statistical software package): The student version for this package can be purchased from the textbook annex at a discounted price. Alternatively, a temporary demonstration version can be downloaded from www.minitab.com. It is also available at computing facilities around campus.
Syllabus Examinations Two midterm exams and a final exam will be given. The final exam is a comprehensive test. Exam I: Thursday, March, 10 in class (Section 02 and 03) Exam II: Thursday, April, 21 in class (Section 02 and 03) Final: To be announce Make-up exam: IF you have a university excuse for missing an exam, you may take make-up exam. It is preferred that you must notify me at least 1 days BEFORE the exam. Also you should take it before the next exam.
Syllabus Assignments Ten Assignments will be asked and 9 assignments are counted except the worst one. Assignments will be handed in the class at the beginning of the lecture on due data.
No late assignments will be accepted. It is necessary to show sufficient calculation steps with the answer to a problem. Grade Assignment 20% Examinations Each 20% Final Exam 40%. What is Statistics? Analysis of data (in short) Design experiments and data collection Summary information from collected data Draw conclusions from data and make decision based on finding. Variables and Data A variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration.
Examples: Body temperature is variable over time or (and) from person to person. Hair color, white blood cell count, time to failure of a computer component. Definitions An experimental unit is the individual or object on which a variable is measured. A measurement results when a variable is actually measured on an experimental unit. A set of measurements, called data, can be either a sample or a population. Basic Concept Population: the set of all measurements of interest to the investigator Sample: a subset of measurements selected from the population of interest.
Example Variable Hair color Experimental unit Person Typical Measurements Brown, black, blonde, etc. Example Variable Time until a light bulb burns out Experimental unit Light bulb Typical Measurements 1500 hours, 1535.5 hours, etc. How many variables have you measured? Univariate data: One variable is measured on a single experimental unit. Bivariate data: Two variables are measured on a single experimental unit.
Multivariate data: More than two variables are measured on a single experimental unit. How many variables have you measured? 14 Bus Jr F 2.6 5 15 Eng Fr M 2.7 4 17 Eng So M 2.9 3 15 Math So F 2.3 2 16 Psy Fr F 2.0 1 # of units Major Year Gender GPA Student. Types of Variables Qualitative Quantitative Discrete Continuous. Types of Variables Qualitative variables measure a quality or characteristic on each experimental unit.
(Categorical Data) Examples: Hair color (black, brown, blonde) Make of car (Dodge, Honda, Ford) Gender (male, female) State of birth (California, Arizona.). Types of Variables Quantitative variables measure a numerical quantity on each experimental unit.
Discrete if it can assume only a finite or countable number of values. Continuous if it can assume the infinitely many values corresponding to the points on a line interval.
Examples For each orange tree in a grove, the number of oranges is measured. Quantitative discrete For a particular day, the number of cars entering a college campus is measured.
Chapter SixDistribusi Probabilitas DDiisskkrreettGOALS1. Define the terms probability distribution andrandom variables.2.
Distinguish between a discrete and continuousprobability distributions.3. Calculate the mean, variance, and standarddeviation of a discrete probability distribution.4. Binomial probability distribution.5. Hypergeometric distribution.6. Poisson distribution.
Distribusi Probabilitas Distribusi Probabilitas: daftar seluruh hasilpercobaan beserta probabilitas untuk masing-masinghasil. Karakteristik Distribusi Probabilitas: Probabilitas sebuah hasil adalah antara 0 dan 1 Semua kejadian (event) adalah mutuallyexclusive Jumlah probabilitas semua kejadian (event) yangmutually exclusive=1 (c o lle c tive ly e xha us tive ) 3.
Contoh:Eksperimen melempar koin 3 kali. KeluarnyaHe a d (H) menjadi fokus, misalnya X adalahkejadian keluar He a d (H).H: hasil lemparan he a d dan T: hasil lemparanta il.Maka, akan ada 8 kemungkinan hasil. Contoh: Eksperimen melempar kointiga kaliPossibleResultLemparan Koin NumberPertama Kedua Ketiga of Heads1 T T T 02 T T H 13 T H T 14 H T T 15 T H H 26 H T H 27 H H T 28 H H H 3 5.
Distribusi ProbabilitasNumber of Heads(X)Probability of OutcomesP(X)0 1/8 = 0,1251 3/8 = 0.3752 3/8 = 0.3753 1/8 = 0,125Total 1 6. Random Variables (VariabelAcak) Variable Acak adalah nilai numerik yangditentukan oleh hasil suatu eksperimen.
Nilainyabisa bermacam-macam. Contoh: Jumlah siswa yang absen pada hari ini, angkanyamungkin 0, 1, 2, 3 dll.
Angka absen adalahvariabel acak Berat tas yang dibawa mahasiswa, mungkin 2,5 kg;3,2kg, dll.berat tas adalah variabel acak. Types of Random Variables A discrete random variable can assumeonly certain outcomes. Usually data wasobtained by counting. A continuous random variable canassume an infinite number of valueswithin a given range.
Usually data wasobtained by measuring. Types of Random Variables Examples of a discrete random variable: The number of students in a class. The number of children in a family. The number of cars entering a carwash in a hour. Number of home mortgages approved by CoastalFederal Bank last week. Number of CDs you own.
Number of trips made outside Hong Kong in thepast one year. The number of ten-cents coins in your pocket. Types of ProbabilityDistributions Examples of a continuous randomvariable: The distance students travel to class. The time it takes an executive to drive to work. The length of an afternoon nap.
The length of time of a particular phone call. The amount of money spent on your lasthaircut. The Mean of a Discrete ProbabilityDistribution The mean: reports the central location of the data. Is the long-run average value of the randomvariable. Is also referred to as its expected value, E(X),in a probability distribution. Is a weighted average. The Mean of a Discrete ProbabilityDistributionThe mean is computed by the formula: = xP(x)where m represents the mean and P(x ) is theprobability of the various outcomes x.Similar to the formula for computing groupedmean where P(x) is replaced by relativefrequency.
The Variance of a DiscreteProbability Distribution The variance measures the amount ofspread (variation) of a distribution. The variance of a discrete distribution isdenoted by the Greek letter s2 (sigmasquared).
The standard deviation is the square rootof s2 13. The Variance & standard deviationof a Discrete ProbabilityDistribution The variance of a discrete probabilitydistribution is computed from the formula:2 = (x - )2P(x) The stadard deviation is the square root of s2 = 2Similar to the formula for computing groupedvariance where P(x) is replaced by relativefrequency. EXAMPLE 2 Arman, owner of College Painters, studied his recordsfor the past 20 weeks and reports the followingnumber of houses painted per week:# o f H o u s e s P a i n t e d Weeks to finish10 511 612 713 2 Set the probability distribution Compute mean and variance 15.
EXAMPLE 2 c o ntinue d Probability Distribution:Number of houses painted, x W e e k s Probability, P(x)10 5.2511 6.3012 7.3513 2.10Total 20 1.00 16. EXAMPLE 2 c o ntinue d Compute the mean number of houses paintedper week: = E(x) =xP(x)(10)(.25) (11)(.30) (12)(.35) (13)(.10)= + + +11.3=x Week P(x) x.P(x)10 5 0.25 2.511 6 0.30 3.312 7 0.35 4.213 2 0.10 1.3Total 20 1 11.3 17. EXAMPLE 2 c o ntinue d Compute the variance of the number ofhouses painted per week: = (x -) P(x)(10 11.3) (.25). (13 11.3) (.10)= - + + -0.4225 0.0270 0.1715 0.2890= + + +0.912 22 2=x Week P(x) x.P(x) x- (x-)2 (x-)2.P(x)10 5 0.25 2.5 -1.3 1.69 0.4211 6 0.30 3.3 -0.3 0.09 0.0312 7 0.35 4.2 0.7 0.49 0.1713 2 0.10 1.3 1.7 2.89 0.29Total 20 1 11.3 0.91 18. Types of Probability Distributions Discrete Probability Distributions Binomial Probability Distributions Hypergeometric Probability Distributions Poisson Probability Distributions Continuous Probability Distributions Normal Probability Distributions 19. Binomial Probability Distribution The binomial distribution has the followingcharacteristics: An outcome of an experiment is classified intoo ne o f TWO m utua lly e x c lus ive c a te g o rie s,such as a success or failure. The data collected are the results of countingthe success event of some trial.
The probability of success stays the same foreach trial. The trials are independent. Binomial Probability Distribution To construct a binomial distribution, let n be the number of trials x be the number of observed successes p be the probability of success on each trial The formula for the binomial probabilitydistribution is:P(x) = nCx p x(1- p)n-x 21. Binomial Probability Distribution The formula for the binomial probabilitydistribution is:P(x) = nCx p x(1- p)n-xTTT, TTH, THT, THH,HTT, HTH, HHT, HHH. X=number of heads The coin is fair, i.e., P(head) = 1/2. P(x=0) = 3C0 0.5 0(1- 0.5)3-0 =0.125=1/8 P(x=1) = 3C1 0.5 1(1- 0.5)3-1 =0.375=3/8 P(x=2) = 3C2 0.5 2(1- 0.5)3-2 =0.375=3/8 P(x=3) = 3C3 0.5 3(1- 0.5)3-3 =0.125=1/8When the coin is not fair, simple counting rule will not work.
EXAMPLE 3The Department of Labor reports that20% of the workforce in Surabaya isunemployed. From a sample of 14workers, calculate the followingprobabilities: Exactly three are unemployed. At least three are unemployed. At least one are unemployed. EXAMPLE 3 c o ntinue dThe Department of Labor reports that 20% of the workforce inSurabaya is unemployed. From a sample of 14 workers The probability of exactly 3:(3) (.20)3 (1.20)11P = C -14 3(364)(.0080)(.0859).2501 The probability of at least 3 is:P x = P + P + P + +P( 3) (3) (4) (5). (14)3 11 14 0C C= + += + + + =(.20) (.80).
(.20) (.80)14 3 14 14.250.172.000 0.551 24. Example 3 c o ntinue dThe Department of Labor reports that 20% of the workforce inSurabaya is unemployed.
From a sample of 14 workers The probability of at least one beingunemploye=d.P(1) + P(2) +.+ P(14)= -= - -= - =0 1414 0P(x 1)1 P(0)1 C (.20) (1.20)1.044.956 25. Mean & Variance of the BinomialDistribution The mean is found by:m =np The variance is found by:s 2 = np (1-p ) 26.
EXAMPLE 4 From EXAMPLE 3, recall that p =.2 and n=14. Hence, the mean is:m= n p = 14(.2) = 2.8. The variance is:s2 = n (1- p ) = (14)(.2)(.8) =2.24. Contoh Probabilitas kerusakan pada barang yangdiproduksi Perusahaan X adalah 10%.Jika diambil 6 sampel random, maka: Buatlah distribusi probabilitas Hitung rata-rata dan standar deviasiprobabilitas tersebut 28. Jumlah BarangRusak (X)Probabilitas, P(X)0 P(0)=6C0 0.10(1- 0.1)6-0 = 0,5311 P(1)=6C1 0.11(1- 0.1)6-1 = 0,3542 P(2)=6C2 0.12(1- 0.1)6-2 =0,0983 0,0154 0,0015 0,0006 0,000Total 1m = np = 6.0,10 = 0,602 (1 ) 6.0,10(1 0,9) 0,54= =s np p= - = - =0,54 0,73s 29. Soal Berdasarkan data yang ada, probabilitasmahasiswa lulus Mata Kuliah Statistikadalah 70%.
Jika diambil sampel random10 mahasiswa, hitung probabilitas:1. 6 mahasiswa lulus2. 3 mahasiswa tidak lulus3. Kurang dari 9 mahasiswa lulus4. Paling banyak 2 mahasiswa tidak lulus 30.
Soal Mahasiswa Lulus n=10; p=0.71. 6 mahasiswa lulus P(6)2. 3 mahasiswa tidak lulus = 7 mahasiswa lulusdengan p=0.7 gunakan x =10-3=7P(7)atau dengan p=1-0.7=0.3 P(3)3.
Kurang dari 9 mahasiswa lulus P(x.