Each of 150 newly manufactured items is examined and the number of scratches per item is recorded (the items are sup- posed 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 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 je 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: u for X Poisson.]