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How independent points uniformly distributed on the square

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Question: An irregularly shaped object of unknown area A is located in the unit square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. Consider a random point distributed uniformly over the square; let Z = 1 if the point lies inside the object and Z = 0 otherwise. Show that E(Z) = A. How could A be estimated from a sequence of n independent points uniformly distributed on the square?

Reference no: EM131731611

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