Each of 174 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:

number of scratches per item 0 1 2 3 4 5 6 7
observed frequency 24 34 48 33 18 7 9 1
let x = the number of scratches on a randomly chosen item, and assume that x has a poisson distribution with parameter μ.

(a) find an unbiased estimator of ? and compute the estimate for the data. [hint: e(x) = ? for x poisson, so
e(x) = ? ]
(b) what is the standard deviation (standard error) of your estimator? compute the estimated standard error. [hint: ? x2 = ? for x poisson.]