This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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? Let’s 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 ˆ 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 = ˆ 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 = = = ) ( ) ˆ ( 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)...
View
Full Document
 Spring '08
 Perevalov
 Normal Distribution, 0.01 mm, 0.05 mM, 0.015 mm

Click to edit the document details