Chapter 6.1, Problem 9E

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

1. a. Find an unbiased estimator of p and compute the estimate for the data. [Hint: E(X) = μ for X Poisson, so E(X) = ?]
2. b. What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint: ${\sigma }_x^2\text{ = }\mu$. for X Poisson.]