Chapter2 - Statistics Statistics for Performance Analysis...

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Statistics for Performance Analysis R. Jain book slides 12-1 ©2006 Raj Jain www.rajjain.com Why Do We Need Statistics? 1. Aggregate data into meaningful information. 2. A single number used to summarize a larger collection of values. 445 446 397 226 388 3445 188 1002 47762 432 54 12 98 345 2245 8839 77492 472 565 999 1 34 882 545 4022 12-2 ©2006 Raj Jain www.rajjain.com 827 572 597 364 ... = x
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Overview ± Basic Probability and Statistics Concepts: CDF, PDF, PMF, Mean, Variance, CoV, Normal Distribution ± Summarizing Data by a Single Number: Mean, Median, and Mode, Arithmetic, Geometric, Harmonic Means Mf A R t i 12-3 ©2006 Raj Jain www.rajjain.com ± Mean of A Ratio ± Summarizing Variability: Range, Variance, percentiles, Quartiles ± Determining Distribution of Data: Quantile-Quantile plots Part III: Probability Theory and Statistics 1. How to report the performance as a single number? Is specifying the mean the correct way? 2. How to report the variability of measured quantities? What are the alternatives to variance and when are they appropriate? 3. How to interpret the variability? How much confidence can you put on data with a large variability? 4. How many measurements are required to get a desired level of statistical confidence? 5. How to summarize the results of several different workloads on a single computer system? 12-4 ©2006 Raj Jain www.rajjain.com 6. How to compare two or more computer systems using several different workloads? Is comparing the mean sufficient? 7. What model best describes the relationship between two variables? Also, how good is the model?
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Basic Probability and Statistics Concepts ± Independent Events : Two events are called independent if the occurrence of one event does not in any way affect the probability of the other event. ± Random Variable : A variable is called a random variable if it takes one of a specified set of values with a specified probability. 12-5 ©2006 Raj Jain www.rajjain.com CDF, PDF, and PMF ± Cumulative Distribution Function : ± Probability Density Function : 1 12-6 ©2006 Raj Jain www.rajjain.com 0 x F(x) f(x) x
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CDF, PDF, and PMF (Cont) ± Given a pdf f(x): ± Probability Mass Function : For discrete random variables: f(x i) 12-7 ©2006 Raj Jain www.rajjain.com x i Mean, Variance, CoV ± Mean or Expected Value : ± Variance : The expected value of the square of distance between x and its mean 12-8 ©2006 Raj Jain www.rajjain.com ± Coefficient of Variation :
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Covariance and Correlation ± Covariance : ± For independent variables, the covariance is zero: ± Although independence always implies zero covariance, the reverse is not true. 12-9 ©2006 Raj Jain www.rajjain.com ± Correlation Coefficient : normalized value of covariance The correlation always lies between -1 and +1. Mean and Variance of Sums ± If are k random variables and if are k arbitrary constants (called weights) then are arbitrary constants (called weights), then: ± For independent variables: 12-10 ©2006 Raj Jain www.rajjain.com
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Quantiles, Median, and Mode ± Quantile : The x value at which the CDF takes a value α is called the α -quantile or 100 α -percentile. It is denoted by x α : ± Median : The 50-percentile or (0.5-quantile) of a random
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This note was uploaded on 10/27/2010 for the course CMPE 474 taught by Professor Muhammedsalamah during the Spring '10 term at Eastern Mediterranean University.

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Chapter2 - Statistics Statistics for Performance Analysis...

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