Question: 2. [10 marks] A book has n typographical errors. Two proofreaders, A and .3, independently read the book and check for errors. A catches each

2. [10 marks] A book has n typographical errors. Two proofreaders,

2. [10 marks] A book has n typographical errors. Two proofreaders, A and .3, independently read the book and check for errors. A catches each error with prob- ability p1 independently. Likewise for B, who has probability p; of catching any given error. Let X1 be the number of typos caught by A, X; be the number caught by B, and X be the number caught by at least one of the two proofreaders. (a) Find the distribution of X. (b) Find E(X). (c) Assuming that p1 = p; = p, nd the eonditional distribution of X1 given that X1 + X2 = m

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