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QMS 102 (186)
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Lecture 8

Lecture 8 (week 9)

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Quantitative Methods
QMS 102
Clare Chua

Key Answers Topics that will be tested in Page 241 Quiz 2: 5.10) E(X)=$80,000 5.11a) Discrete Probability # years X P(X) 1 $2.00 0.5 Binomial Probability 2 3.50 0.2 Poisson Probability 3 4.50 0.2 5 6.50 0.1 Normal Probability 5.11b) $406.25 Q5.14) Tire C 5.12a) Project 3 b) Project 3 Q 5.15) Order 11 units 5.13) Country C Which of the above probability distributions are for a discrete random variable? Continuous? Discrete Continuous Binomial Probability Distribution Binomial Normal Poisson Inverse Normal Central Limit Theorem Addicreterandom variabe may assume either a finite number How to differentiate between of values or an infinite sequence of values. discrete and continuous random Discrete variables? CONTINUOUS Random Variables DISCRETE The observation can be The observation can be counted measured Example: the number of EExamplleTiime ((iin students who drive to seconds) is measured and FINITE INFINITE school not counted. Number of values Number of values What is the probability What is the probability that at most 110 students that the download time for will drive to school? a home page on a Web browser is between 7 and 10 seconds? 1 Discrete Random Variable Examples: Finite/Infinite number values Experiment Random Possible What is a Binomial Probability Variable Value s Maake 1100sales calslls# Saless 0,1,,2,, .1000.,, 1 Distribution? Fiiniitte Inspect 70 radios # Defective 0, 1, 2, ..., 70 Number values Answer 33 questions # Correct 0, 1, 2, ..., 33 Count cars at toll # Cars 0, 1, 2, ..., B between 11:00 & 1:00 arrivin g Infinite Number values Characteristics of the Binomial Distribution Summary: Three pieces of info 1. The experiment consists of a sequence of n identical trials (repetitions). 2. Each trial has only one of the two possible mutually 1. Sequence of n identical trials / A sample of n exclusive outcomes, success or a failure. Two items are selected from a large population outcomes, success and failure, are possible on each 2. Constant Probability (!) for each Trial trial. eg..Probabiiy ofgettnga aiillhee ame each time we toss the coin and each light bulb has the 3. The probability of each outcome does not change same probability of being defective from trial to trial. 4. The trials are independent, thus we must sample with 3. Each trial has 2 outcomes replacement. Success (desired outcome) or failure The random variable that we are interested in is, X= # of successes To calculate the probability that X takes on a Number of successesin a sample specific value we use the Binomial Probability of n observations (trials) Distribution Function X= # of successes Use the CASIO calculator to obtain the What is the Binomial Probability Binomial Probability See Handout on CASIO Calculator Lesson 3 : Distribution Function? Binomial and Poisson page 250 n! x n x Using the CASIO calculator P ( x) 5 (1 ) x!( )! STAT F5(DIST) F5(BINM) F1(Bpd) P(X=x) = probability that x successes given a knowledge of Then select the following options n and ! You will see: Binomial P.D X = number of successes in Data : Variable sample, (X = 0, 1, 2, ..., n) X : Numtrial : 5 = probability of each success P : n = sample size Save Res: None Execute 2 www.notesolution.comBpd and Bcd functions Use the CASIO calculator to obtain the The Casio calculator has 2 Binomial Probability Binomial Probability functions programmed into its memory. Experiment: Toss 1 coin 6 times in a row.. These are: Whats the probability of getting 2 tails? See Handout on CASIO Calculator 1) Bpd stands for Binomial Probability Distribution. This function calculators a Binomial Probability of the form: Lesson 3 : Binomial and Poisson page 250 X= #offaiillssTTAT FF5(DIST))F5(BINM)) F1(Bppd)) P((X= #)) n = 6 Then select the following options
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