Suppose that the number of typographical errors in a new text is Poisson distributed with mean 1 answer below »

Suppose that the number of typographical errors in a new text is Poisson distributed with mean λ. Two proofreaders independently read the text. Suppose that each error is independently found by proofreader i with probability pi , i = 1, 2. Let X1 denote the number of errors that are found by proofreader 1 but not by proofreader 2. Let X2 denote the number of errors that are found by proofreader 2 but not by proofreader 1. Let X3denote the number of errors that are found by both proofreaders. Finally, let X4 denote the number of errors found by neither

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proofreader.

(a) Describe the joint probability distribution of X1,X2,X3,X4.

(b) Show that

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Suppose now that λ, p1, and p2 are all unknown.

(c) By using Xi as an estimator of E[Xi ], i = 1, 2, 3, present estimators of p1, p2, and λ.

(d) Give an estimator of X4, the number of errors not found by either proofreader.

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