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Each of 180 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 2 4 5 7 Observed frequency 23 39 39 38 16 9 13 3 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) = µ 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 standard error. [Hint: oy = µ for X Poisson.] (Round your answer to three deci 2

Each of 180 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 2 4 5 7 Observed frequency 23 39 39 38 16 9 13 3 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) = µ 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 standard error. [Hint: oy = µ for X Poisson.] (Round your answer to three deci 2

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Each of 180 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 1 2 6 7 Observed frequency 23 39 39 38 16 13 3 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) = µ for X Poisson, so E(X) = ?] (Round your answer to two decimal places.) 2 (b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint: ox = u for X Poisson.] (Round your answer to three decimal places.
Transcribed Image Text:Each of 180 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 1 2 6 7 Observed frequency 23 39 39 38 16 13 3 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) = µ for X Poisson, so E(X) = ?] (Round your answer to two decimal places.) 2 (b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint: ox = u for X Poisson.] (Round your answer to three decimal places.
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