6, -2 points 9 6.E.005 My Notes Ask Your Each uf 155 newly ufacture ies is exaia

Question

6, -2 points 9 6.E.005 My Notes Ask Your Each uf 155 newly ufacture ies is exaiarid lhe number of scraluhes per is reode (Uhe iles are suppoed lo be free ofscralhes), yieldin Lhe following dala: Number of per ite 1 2 34 5 6 7 requercy 12 36 37 27 10 14 14 5 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 [Hnr: E X E(x) - for X Poisson, so E x ? (Round your answer to two decimal places.) (b) What is the standard deviation (standard error) of your estimator? Compute the estimated stadard erront:x -forXPoisson.] (Round your answer to three decimal places.) Need Help?RTalk to a Tutor

Explanation / Answer

a)The unbiased estimator for µ is the mean = E(X)

E(X) = (0*12 +1*36+ 2*37+ 3*27+ 4*10+5*14+6*14+7*5)/155

= 2.709677

b) For a poisson random variable, Mean = Variance = µ

Standard error of the estimator = V( x) = (µ / n) = (2.709677/155) = 0.13222

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