reasons for being used in different practical cases: – Normal: measurement & dimension data – Lognormal: manual service & repair times – Poisson: # of events occurring in a time period‚ distance‚ or area – Exponential‚ Weibull: Time to failure of equipment Ch. 5: Discrete Distributions 1. Uniform 2. Binomial 3. Hypergeometric 4. Negative Binomial 5. Geometric 6. Poisson SKIPPING: Multinomial (p/149-150) Discrete Uniform Distribution Bernoulli Process Binomial Distribution f(x;n‚p)= =average
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Chapter 7 Survival Models Our final chapter concerns models for the analysis of data which have three main characteristics: (1) the dependent variable or response is the waiting time until the occurrence of a well-defined event‚ (2) observations are censored‚ in the sense that for some units the event of interest has not occurred at the time the data are analyzed‚ and (3) there are predictors or explanatory variables whose effect on the waiting time we wish to assess or control. We start with some
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Problem 1 A gas station with only one gas pump employs the following policy: if a customer has to wait‚ the price is $3.50 per gallon; if they don’t have to wait‚ the price is $4.00 per gallon. Customers arrive according to a Poisson process with a mean rate of 20 per hour. Service times at the pump have an exponential distribution with a mean of 2 minutes. Arriving customers always wait until they can by gasoline. Determine the expected price of gasoline per gallon. Problem 3 The Old Colony theme
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2012 2012 Feloz and fellow statisticians Felix MAIKO I63/28541/2009 [ QUEUING THEORY AND ITS APPLICATION:ANALYSIS OF THE SALES CHECKOUT OPERATION IN NAKUMATT HIGHRIDGE SUPERMARKET] This paper contains the analysis of Queuing systems for the empirical data of supermarket checkout service unit as an example. One of the expected gains from studying queuing systems is to review the efficiency of the models in terms of utilization and waiting length‚ hence increasing the number
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SIMULATION SOFTWARE June 2012 2a)Consider the grocery store with one check out counter. Prepare the simulation table for eight customers and find out average waiting time of customer in queue‚idle time of server and average service time .The inter arrival time (IAT) and service time (ST) are given in minutes. IAT : 3‚2‚6‚4‚4‚5‚8 ST(min) :3‚5‚5‚8‚4‚6‚2‚3 Assume first customer arrives at time t=0 10 M 2b) Suppose the maximum inventory level is M 11 units and the review period is 5 days estimate
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Change - 1 Explain the scales of measurement in details ‚ giving examples: Data has been classified into four scales of measurement so that it can be easily interpreted universally. The scale is chosen depending on the information that the data is intending to represent. The four scales of measurement of data are nominal‚ ordinal‚ interval‚ and ratio. Each plays a different‚ yet very important role in the world of statistic a) Nominal scale Is the lowest level in scales of measurement
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probability (3%) 1. Explain why the distribution B(n‚p) can be approximated by Poisson distribution with parameter if n tends to infinity‚ p 0‚ and = np can be considered constant. 2. Show that – and + are the turning points in the graph of the p.d.f. of normal distribution with mean and standard deviation . 3. What is the relationship between exponential distribution and Poisson distribution? II. Computation of probability (7%) 1. Let the random variable
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EXERCISES (Discrete Probability Distribution) EXERCISES (Discrete Probability Distribution) P X x n C x p 1 p x BINOMIAL DISTRIBUTION n x P X x n C x p 1 p x BINOMIAL DISTRIBUTION n x 1. 2. 3. The probability that a certain kind of component will survive a given shock test is ¾. Find the probability that exactly 2 of the next 4 components tested survive. The probability that a log-on to the network is successful is 0.87. Ten users
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n=100 p=0.02 ‚ 100c3‚ 0.02^3‚ (0.98)^97= 0.182 Poisson distribution- close relative of the bionomial distribution and can be used to approximate it when The number of trials‚ n is large The probability of success‚ p‚ is small Also useful for solving problems where events occur at random Main difference between the bionomial and poisson distributions is that the bionomial distribution uses the probabilities of both success and failure‚ while the poisson uses only the probability of successes. P(
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Sive By John B. Keane * ‘Sive’ is set in Ireland in the middle of the 20th Century. The action of the play takes place in a small farmhouse in a remote part of County Kerry which is home to the Glavin family. * Poverty is made obvious in the opening stage directions “the kitchen is poorly furnished” * The relationships between the Glavin family members are strained. The hostility that exists between Mena and her mother-in-law‚ Nanna‚ is obvious from the very beginning of the play
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