9. Each of 150 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 18 37 42 30 13 7 2 1 Let Xthe number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter l.

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

b. What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. (Hint:  l for X Poisson.)