Each of 146 newly manufactured items is examined and the num

Each of 146 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:

Let X = the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter .

(a) Find an unbiased estimator of and compute the estimate for the data. [Hint: E(X) = for X Poisson, so

E(X) = ?]

(Round your answer to four decimal places.)

(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 five decimal places.)

Number of
scratches
per item	0	1	2	3	4	5	6	7
Observed
frequency	19	30	38	26	11	7	11	4

a) Unbiased estimator is sample mean = 20.8571

b) Variance for Poisson = mean = 20.8571

Std dev = 4.56696

x	0	1	2	3	4	5	6	7	Total
f	19	30	38	26	11	7	14	1	146

		Mean	20.8571

Each of 146 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

Each of 146 newly manufactured items is examined and the num

Solution

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