Each of 146 newly manufactured items is examined and the number of scratches per

Question

Each of 146 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:

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 and compute the estimate for the data. [Hint: E(X) = for X Poisson, so

E(X) = ?]

(Round your answer to four decimal places.)

(b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint: X2 = for X Poisson.] (Round your answer to five decimal places.)

Number of scratches per item 0 1 2 3 4 5 6 7 Observed frequency 19 30 38 26 11 7 11 4

Explanation / Answer

a) Unbiased estimator is sample mean = 20.8571

b) Variance for Poisson = mean = 20.8571

Std dev = 4.56696

x 0 1 2 3 4 5 6 7 Total f 19 30 38 26 11 7 14 1 146 Mean 20.8571

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.