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Unformatted text preview: 1 Parameter estimation: example Suppose that out of 1 million relays exactly 2.5% (or 25000) are defective, but we do not know that. We would like to estimate that percentage by inspecting a relatively small sample. What should we do? Lets simulate random sampling from that populaton (can use Excel). 2 Estimation of proportion Large population of objects Every object can be defective with probability of p independently of the other objects We can select a sample of size n from the population How can we estimate p from the sample? 3 Example 1 The 1700 ship insurer knows out of 755 ships that sailed from the local port 10 were lost at sea. What is the point estimate of the probability p that a ship can be lost at sea? p 4 Example 2 A company wants to estimate the percentage of defective (out of spec) shafts produced by a new superfast technology. The trial run of 500 shafts ended up in 3 of them being out of spec. What is the point estimate of the proportion of defective shafts for this process? 5 Point estimator of proportion Sample of size n was taken The number of defective items in the sample is X Then the point estimator of the proportion of defective is n X p = 6 Why this estimator Unbiased estimator: In other words, the long run average of the estimated proportion is the true one p n np n X E p E = = = ) ( ) ( 7 Parameter estimation: example 2 A machine is producing shafts with the mean diameter 0.512 mm and the standard deviation of 0.015 mm (and approximately normally distributed)...
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This note was uploaded on 03/17/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .
 Spring '08
 Perevalov

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