62. 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 . Let denote the number of errors that are found by proofreader 1 but not by proofreader 2.

Let denote the number of errors that are found by proofreader 2 but not by proofreader 1. Let denote the number of errors that are found by both proofreaders. Finally, let denote the number of errors found by neither proofreader.

(a) Describe the joint probability distribution of

.

(b) Show that Suppose now that , and are all unknown.

(c) By using as an estimator of , present estimators of , and λ.

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