Suppose three marksmen shoot at a target the ith marksman, Basic Statistics

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Suppose three marksmen shoot at a target the ith marksman

Question: Suppose three marksmen shoot at a target. The ith marksman fires n_i times, hitting the target each time with probability p, independently of his other shots and the shots of the other marksmen. Let X be the total number of times the target is hit.

a) Is the distribution of X binomial?

b) Find E(X) and Vαr(X).

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Basic Statistics: Suppose three marksmen shoot at a target the ith marksman

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Basic Statistics: Suppose three marksmen shoot at a target the ith marksman

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