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Unformatted text preview: 36226 Summer 2010Homework 4Due July 121. Assume thatX, the proportion of defective products that a machine produces in a day, hasthe following density:fX(x) =(1x)1I(0,1)(x).Note that this is a Beta(1,) distribution.In order to estimate, the machine was observed for 100 days and the proportion of defectiveproducts was recorded for each day. The data is in theRfileDefects.Rdatathat is linkedfrom the HW section of the course website. The name of the dataset isdefects. It is avector with 100 entries.(a) Find a method of momentsestimatorforbased on a random sample of sizenfrom theabove distribution.(b) Find a maximum likelihoodestimatorfor.(c) Use part (a) and the data to find anestimatefor.(d) Use part (b) and the data to find a secondestimatefor.(e) Use your estimates from part (c) and (d) to estimate the probability that on a givenday, the proportion of defective products will exceed .0252. LetX1,X2,...,Xnbe a random sample from the following distribution:fX(x) =...
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 Summer '09

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