Solved: The article The Prediction of Corrosion by

Chapter 4, Problem 109

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The article The Prediction of Corrosion by StatisticalAnalysis of Corrosion Profiles (Corrosion Science,1985: 305315) suggests the following cdf for the depthX of the deepest pit in an experiment involving the exposureof carbon manganese steel to acidified seawater.F(x; a, b) 5 e2e2(x2a)yb2` , x , `The authors propose the values a 5 150 and b 5 90.Assume this to be the correct model.a. What is the probability that the depth of the deepestpit is at most 150? At most 300? Between 150 and300?b. Below what value will the depth of the maximum pitbe observed in 90% of all such experiments?c. What is the density function of X?d. The density function can be shown to be unimodal (asingle peak). Above what value on the measurementaxis does this peak occur? (This value is the mode.)e. It can be shown that E(X) < .5772b 1 a. What is themean for the given values of a and b, and how doesit compare to the median and mode? Sketch the graphof the density function. [Note: This is called the largestextreme value distribution.]