Each of 177 newly manufactured items is examined and the number of scratches per

Question

Each of 177 newly manufactured items is examined and the number of scratches per item is recorded (the items are supposed to be free of scratches), yielding the following data Mumber of scratches per item Observed frequency 15 15 39 15 11 4 1 Let X-the number of scratches on a randomly chosen item, and assume that X has a poisson distribution with parameter . a Find an unhiased estimator o and compute the estimate for the data. Hint: F X·tor X Pois an, so F x Round your answer to two decimal p aces. (b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint: x2- for X Poisson. (Round your answer to three decimal places.) Need Help?Read It[Talk to a Tutor

Explanation / Answer

a) from above distribution:

from above unbiased estimate =417/177=2.36

b) std deviation =(2.36)1/2 =1.536 (please try 1.535 if that does not work due to rounding errror)

x freq(f) x*f 0 15 0 1 45 45 2 44 88 3 39 117 4 15 60 5 11 55 6 4 24 7 4 28 total 177 417

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