Each of 166 newly manufactured items is examined and the number of scratches per

Question

Each of 166 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 folowing dera Number of per item 1 2 34 56 7 Coserved frequency 18 43 4333 15 653 Let X- the number of scratches on a randomly chosen item, and assume that Xhas a Poisson distributan th paratrieter (a) Find an unbiased estimator or and compute the estimate for the data, tiint Etx- for x Poason, so Etn-7nRound your answer to two ocmai Places hint: e 2·M for X Polsson.] CRond yo r ars wer to three decimal paces.) b) what is the standard deviation (standard error) of your estimator? Compute the esti 1491 X ated standard emor Need Help? s r

Explanation / Answer

f= 166

fx = 369

Mean = fx / f = 2.2229

Mean square = f x^2 / f = 7.4036

Variance = (Mean square) - (Mean)^2

Variance = f x^2 - Mean^2 = 2.462

Stadard Dev= Var = 1.569

Values ( X ) Frequency(f) fx ( X^2) f x^2 0 18 0 0 0 1 43 43 1 43 2 43 86 4 172 3 33 99 9 297 4 15 60 16 240 5 6 30 25 150 6 5 30 36 180 7 3 21 49 147

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