. e Homel Chegg.com × \\ p WeBWorkf17dpavlovm x/ yi HW11 C www.webassign.net/web

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. e Homel Chegg.com × p WeBWorkf17dpavlovm x/ yi HW11 C www.webassign.net/web/Student/Assignment-Responses submit?dep: 17474229 6. + -12 points DevoreStat9 6.E.009 My Notes Ask Your Teacher Each of 168 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 Observed frequency 25 30 46 36 12 10 81 0 123 4 56 7 Let X-the number of scratches on a randomly chosen item, and assume that 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 two decimal place (b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error [Hint: Ox2 places.) for X Poisson.] (Round your answer to three decimal Need Help? Radlt_ LTalktoaTutol Submit Assignment Save Assignment Progress Home My Assignments Extension Request webAssOn® 4 0 1997-2017 Advanced Instructional Systems. Inc All rights reserved O Type here to search 11/14/2017

Explanation / Answer

Solution:-

a) E(x) = [ 0(25)+1(30)+2(46)+3(36)+4(12)+5(10)+6(8)+7(1)]/168 = 2.28

b) For a Poisson r.v. E(X) = V(X) = . However, we need V (x¯) = / n

ˆ = sqrt(2.28/168) = 0.116

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