Question

Each of 157 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 16 38 35 37 17 7 6 1 Let X = the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter u. (a) Find an unbiased estimator of u and compute the estimate for the data. (Hint: E(X) = u for X Poisson, so E) = ?] (Round your answer to two decimal places.) (b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. (Hint: 02 = u for X Poisson.] (Round your answer to three decimal places.)

Answer 1

from above:

x	f	f*M	f*M2
0	16	0	0
1	38	38	38
2	35	70	140
3	37	111	333
4	17	68	272
5	7	35	175
6	6	36	216
7	1	7	49
total	157	365	1223
	mean =	x̅=Σf*M/Σf		=	2.3248

a)

from above unbiased estimator of mean =2.32

b)

estimated standard error =√(2.32/157) =0.122